%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL163-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n026.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 17:24:41 EDT 2024

% Result   : Unsatisfiable 0.46s 0.68s
% Output   : Proof 0.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : LCL163-1 : TPTP v8.2.0. Released v1.0.0.
% 0.08/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n026.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 27 22:48:39 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.46/0.68  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.mCQRm8KXKT/cvc5---1.0.5_6830.smt2
% 0.46/0.68  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.mCQRm8KXKT/cvc5---1.0.5_6830.smt2
% 0.54/0.76  (assume a0 (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))))
% 0.54/0.76  (assume a1 (forall ((X $$unsorted)) (= (tptp.xor X tptp.falsehood) X)))
% 0.54/0.76  (assume a2 (forall ((X $$unsorted)) (= (tptp.xor X X) tptp.falsehood)))
% 0.54/0.76  (assume a3 (forall ((X $$unsorted)) (= (tptp.and_star X tptp.truth) X)))
% 0.54/0.76  (assume a4 (forall ((X $$unsorted)) (= (tptp.and_star X tptp.falsehood) tptp.falsehood)))
% 0.54/0.76  (assume a5 (forall ((X $$unsorted)) (= (tptp.and_star (tptp.xor tptp.truth X) X) tptp.falsehood)))
% 0.54/0.76  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))))
% 0.54/0.76  (assume a7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))))
% 0.54/0.76  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.76  (assume a9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))))
% 0.54/0.76  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.76  (assume a11 (= (tptp.not tptp.truth) tptp.falsehood))
% 0.54/0.76  (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))))
% 0.54/0.76  (assume a13 (not (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))))
% 0.54/0.76  (step t1 (cl (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (not (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (not (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (not (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (not (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (not (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (not (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (not (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule and_neg)
% 0.54/0.76  (step t2 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule implies_neg1)
% 0.54/0.76  (anchor :step t3)
% 0.54/0.76  (assume t3.a0 (= tptp.falsehood (tptp.not tptp.truth)))
% 0.54/0.76  (assume t3.a1 (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)))
% 0.54/0.76  (assume t3.a2 (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.a3 (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))))
% 0.54/0.76  (assume t3.a4 (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))))
% 0.54/0.76  (assume t3.a5 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.a6 (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)))
% 0.54/0.76  (assume t3.a7 (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)))
% 0.54/0.76  (assume t3.a8 (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))
% 0.54/0.76  (assume t3.a9 (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)))
% 0.54/0.76  (assume t3.a10 (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)))
% 0.54/0.76  (assume t3.a11 (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)))
% 0.54/0.76  (assume t3.a12 (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)))
% 0.54/0.76  (assume t3.a13 (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))))
% 0.54/0.76  (assume t3.a14 (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.a15 (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))))
% 0.54/0.76  (assume t3.a16 (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)))
% 0.54/0.76  (assume t3.a17 (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)))
% 0.54/0.76  (assume t3.a18 (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))
% 0.54/0.76  (assume t3.a19 (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.a20 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))
% 0.54/0.76  (assume t3.a21 (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.a22 (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)))
% 0.54/0.76  (assume t3.a23 (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)))
% 0.54/0.76  (assume t3.a24 (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))))
% 0.54/0.76  (assume t3.a25 (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))))
% 0.54/0.76  (assume t3.a26 (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.a27 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))))
% 0.54/0.76  (assume t3.a28 (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.a29 (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)))
% 0.54/0.76  (assume t3.a30 (= tptp.x (tptp.xor tptp.x tptp.falsehood)))
% 0.54/0.76  (assume t3.a31 (= tptp.y (tptp.xor tptp.y tptp.falsehood)))
% 0.54/0.76  (assume t3.a32 (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)))
% 0.54/0.76  (assume t3.a33 (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))
% 0.54/0.76  (assume t3.a34 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))
% 0.54/0.76  (step t3.t1 (cl (=> (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :rule implies_neg1)
% 0.54/0.76  (anchor :step t3.t2)
% 0.54/0.76  (assume t3.t2.a0 (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))))
% 0.54/0.76  (assume t3.t2.a1 (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))))
% 0.54/0.76  (assume t3.t2.a2 (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a3 (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)))
% 0.54/0.76  (assume t3.t2.a4 (= tptp.y (tptp.xor tptp.y tptp.falsehood)))
% 0.54/0.76  (assume t3.t2.a5 (= tptp.falsehood (tptp.not tptp.truth)))
% 0.54/0.76  (assume t3.t2.a6 (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)))
% 0.54/0.76  (assume t3.t2.a7 (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a8 (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)))
% 0.54/0.76  (assume t3.t2.a9 (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a10 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))
% 0.54/0.76  (assume t3.t2.a11 (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a12 (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)))
% 0.54/0.76  (assume t3.t2.a13 (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a14 (= tptp.x (tptp.xor tptp.x tptp.falsehood)))
% 0.54/0.76  (assume t3.t2.a15 (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)))
% 0.54/0.76  (assume t3.t2.a16 (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a17 (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.t2.a18 (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))))
% 0.54/0.76  (assume t3.t2.a19 (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.t2.a20 (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a21 (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)))
% 0.54/0.76  (assume t3.t2.a22 (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))
% 0.54/0.76  (assume t3.t2.a23 (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))))
% 0.54/0.76  (assume t3.t2.a24 (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.t2.a25 (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))))
% 0.54/0.76  (assume t3.t2.a26 (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.t2.a27 (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))
% 0.54/0.76  (assume t3.t2.a28 (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))))
% 0.54/0.76  (assume t3.t2.a29 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))
% 0.54/0.76  (assume t3.t2.a30 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.t2.a31 (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)))
% 0.54/0.76  (assume t3.t2.a32 (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (assume t3.t2.a33 (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))))
% 0.54/0.76  (assume t3.t2.a34 (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.76  (step t3.t2.t1 (cl (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule symm :premises (t3.t2.a32))
% 0.54/0.76  (step t3.t2.t2 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.t1))
% 0.54/0.76  (step t3.t2.t3 (cl (= (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.a31))
% 0.54/0.76  (step t3.t2.t4 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule symm :premises (t3.t2.t3))
% 0.54/0.76  (step t3.t2.t5 (cl (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.implies tptp.x tptp.y))) :rule symm :premises (t3.t2.a17))
% 0.54/0.76  (step t3.t2.t6 (cl (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.t5))
% 0.54/0.76  (step t3.t2.t7 (cl (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth tptp.y))) :rule refl)
% 0.54/0.76  (step t3.t2.t8 (cl (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) :rule cong :premises (t3.t2.t6 t3.t2.t7))
% 0.54/0.76  (step t3.t2.t9 (cl (= tptp.truth tptp.truth)) :rule refl)
% 0.54/0.76  (step t3.t2.t10 (cl (= (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule cong :premises (t3.t2.t8 t3.t2.t9))
% 0.54/0.76  (step t3.t2.t11 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule trans :premises (t3.t2.t4 t3.t2.t10))
% 0.54/0.76  (step t3.t2.t12 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule cong :premises (t3.t2.t11 t3.t2.t7))
% 0.54/0.76  (step t3.t2.t13 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule symm :premises (t3.t2.a30))
% 0.54/0.76  (step t3.t2.t14 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.t13))
% 0.54/0.76  (step t3.t2.t15 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.a29))
% 0.54/0.76  (step t3.t2.t16 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule symm :premises (t3.t2.t15))
% 0.54/0.76  (step t3.t2.t17 (cl (= (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule symm :premises (t3.t2.a28))
% 0.54/0.76  (step t3.t2.t18 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule symm :premises (t3.t2.t17))
% 0.54/0.76  (step t3.t2.t19 (cl (= tptp.x tptp.x)) :rule refl)
% 0.54/0.76  (step t3.t2.t20 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) :rule symm :premises (t3.t2.a27))
% 0.54/0.76  (step t3.t2.t21 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule symm :premises (t3.t2.t20))
% 0.54/0.76  (step t3.t2.t22 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.a26))
% 0.54/0.76  (step t3.t2.t23 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.t22))
% 0.54/0.76  (step t3.t2.t24 (cl (= (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.a25))
% 0.54/0.76  (step t3.t2.t25 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule symm :premises (t3.t2.t24))
% 0.54/0.76  (step t3.t2.t26 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule symm :premises (t3.t2.a24))
% 0.54/0.76  (step t3.t2.t27 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) tptp.falsehood)) :rule symm :premises (t3.t2.a23))
% 0.54/0.76  (step t3.t2.t28 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) tptp.falsehood)) :rule trans :premises (t3.t2.t26 t3.t2.t27))
% 0.54/0.76  (step t3.t2.t29 (cl (= (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (tptp.and_star tptp.x tptp.falsehood))) :rule cong :premises (t3.t2.t19 t3.t2.t28))
% 0.54/0.76  (step t3.t2.t30 (cl (= (tptp.and_star tptp.x tptp.falsehood) tptp.falsehood)) :rule symm :premises (t3.t2.a22))
% 0.54/0.76  (step t3.t2.t31 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.truth))) :rule trans :premises (t3.t2.t23 t3.t2.t25 t3.t2.t29 t3.t2.t30 t3.t2.a5 t3.t2.a6))
% 0.54/0.76  (step t3.t2.t32 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.truth)))) :rule cong :premises (t3.t2.t9 t3.t2.t31))
% 0.54/0.76  (step t3.t2.t33 (cl (= (tptp.xor tptp.truth tptp.truth) (tptp.not tptp.truth))) :rule symm :premises (t3.t2.a6))
% 0.54/0.76  (step t3.t2.t34 (cl (= (tptp.not tptp.truth) tptp.falsehood)) :rule symm :premises (t3.t2.a5))
% 0.54/0.76  (step t3.t2.t35 (cl (= (tptp.xor tptp.truth tptp.truth) tptp.falsehood)) :rule trans :premises (t3.t2.t33 t3.t2.t34))
% 0.54/0.76  (step t3.t2.t36 (cl (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.truth)) (tptp.xor tptp.truth tptp.falsehood))) :rule cong :premises (t3.t2.t9 t3.t2.t35))
% 0.54/0.76  (step t3.t2.t37 (cl (= (tptp.xor tptp.truth tptp.falsehood) tptp.truth)) :rule symm :premises (t3.t2.a21))
% 0.54/0.76  (step t3.t2.t38 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) tptp.truth)) :rule trans :premises (t3.t2.t21 t3.t2.t32 t3.t2.t36 t3.t2.t37))
% 0.54/0.76  (step t3.t2.t39 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule cong :premises (t3.t2.t7 t3.t2.t38))
% 0.54/0.76  (step t3.t2.t40 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth) (tptp.xor tptp.truth tptp.y))) :rule symm :premises (t3.t2.a20))
% 0.54/0.76  (step t3.t2.t41 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.xor tptp.truth tptp.y))) :rule trans :premises (t3.t2.t39 t3.t2.t40))
% 0.54/0.76  (step t3.t2.t42 (cl (= (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) :rule cong :premises (t3.t2.t19 t3.t2.t41))
% 0.54/0.76  (step t3.t2.t43 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) :rule trans :premises (t3.t2.t12 t3.t2.t14 t3.t2.t16 t3.t2.t18 t3.t2.t42))
% 0.54/0.76  (step t3.t2.t44 (cl (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule cong :premises (t3.t2.t43))
% 0.54/0.76  (step t3.t2.t45 (cl (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule symm :premises (t3.t2.a19))
% 0.54/0.76  (step t3.t2.t46 (cl (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.a16))
% 0.54/0.76  (step t3.t2.t47 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.implies tptp.x tptp.y))) :rule trans :premises (t3.t2.t2 t3.t2.t44 t3.t2.t45 t3.t2.t46 t3.t2.t5))
% 0.54/0.76  (step t3.t2.t48 (cl (= (tptp.implies tptp.x tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule symm :premises (t3.t2.t47))
% 0.54/0.76  (step t3.t2.t49 (cl (= tptp.y tptp.y)) :rule refl)
% 0.54/0.76  (step t3.t2.t50 (cl (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y))) :rule cong :premises (t3.t2.t48 t3.t2.t49))
% 0.54/0.76  (step t3.t2.t51 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y))) :rule symm :premises (t3.t2.a34))
% 0.54/0.76  (step t3.t2.t52 (cl (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule symm :premises (t3.t2.t51))
% 0.54/0.76  (step t3.t2.t53 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule symm :premises (t3.t2.a33))
% 0.54/0.76  (step t3.t2.t54 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule symm :premises (t3.t2.t53))
% 0.54/0.76  (step t3.t2.t55 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule cong :premises (t3.t2.t7 t3.t2.t47))
% 0.54/0.76  (step t3.t2.t56 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)) (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)))) :rule symm :premises (t3.t2.a18))
% 0.54/0.76  (step t3.t2.t57 (cl (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule symm :premises (t3.t2.t46))
% 0.54/0.76  (step t3.t2.t58 (cl (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x) tptp.truth))) :rule cong :premises (t3.t2.a15 t3.t2.t9))
% 0.54/0.76  (step t3.t2.t59 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) :rule symm :premises (t3.t2.a15))
% 0.54/0.76  (step t3.t2.t60 (cl (= (tptp.xor tptp.x tptp.falsehood) tptp.x)) :rule symm :premises (t3.t2.a14))
% 0.54/0.76  (step t3.t2.t61 (cl (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule symm :premises (t3.t2.t60))
% 0.54/0.76  (step t3.t2.t62 (cl (= tptp.falsehood (tptp.xor tptp.truth tptp.truth))) :rule symm :premises (t3.t2.t35))
% 0.54/0.76  (step t3.t2.t63 (cl (= (tptp.xor tptp.x tptp.falsehood) (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)))) :rule cong :premises (t3.t2.t19 t3.t2.t62))
% 0.54/0.76  (step t3.t2.t64 (cl (= (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth) (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)))) :rule symm :premises (t3.t2.a13))
% 0.54/0.76  (step t3.t2.t65 (cl (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule symm :premises (t3.t2.t64))
% 0.54/0.76  (step t3.t2.t66 (cl (= (tptp.xor tptp.x tptp.truth) (tptp.xor tptp.truth tptp.x))) :rule symm :premises (t3.t2.a12))
% 0.54/0.76  (step t3.t2.t67 (cl (= (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule cong :premises (t3.t2.t66 t3.t2.t9))
% 0.54/0.76  (step t3.t2.t68 (cl (= (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)))) :rule symm :premises (t3.t2.a11))
% 0.54/0.76  (step t3.t2.t69 (cl (= tptp.x (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)))) :rule trans :premises (t3.t2.t61 t3.t2.t63 t3.t2.t65 t3.t2.t67 t3.t2.t68))
% 0.54/0.76  (step t3.t2.t70 (cl (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)))) :rule cong :premises (t3.t2.t69 t3.t2.t7))
% 0.54/0.76  (step t3.t2.t71 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x) (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)))) :rule trans :premises (t3.t2.t59 t3.t2.t70))
% 0.54/0.76  (step t3.t2.t72 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x) tptp.truth) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule cong :premises (t3.t2.t71 t3.t2.t9))
% 0.54/0.76  (step t3.t2.t73 (cl (= (tptp.implies tptp.x tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule trans :premises (t3.t2.t6 t3.t2.t57 t3.t2.t58 t3.t2.t72))
% 0.54/0.76  (step t3.t2.t74 (cl (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule cong :premises (t3.t2.t73 t3.t2.t7))
% 0.54/0.76  (step t3.t2.t75 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)))) :rule symm :premises (t3.t2.a10))
% 0.54/0.76  (step t3.t2.t76 (cl (= (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) :rule symm :premises (t3.t2.a9))
% 0.54/0.76  (step t3.t2.t77 (cl (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule symm :premises (t3.t2.t76))
% 0.54/0.76  (step t3.t2.t78 (cl (= (tptp.xor tptp.y tptp.truth) (tptp.xor tptp.truth tptp.y))) :rule symm :premises (t3.t2.a8))
% 0.54/0.76  (step t3.t2.t79 (cl (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule symm :premises (t3.t2.t78))
% 0.54/0.76  (step t3.t2.t80 (cl (= (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule cong :premises (t3.t2.t79 t3.t2.t9))
% 0.54/0.76  (step t3.t2.t81 (cl (= (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth) (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)))) :rule symm :premises (t3.t2.a7))
% 0.54/0.76  (step t3.t2.t82 (cl (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor tptp.y tptp.falsehood))) :rule cong :premises (t3.t2.t49 t3.t2.t35))
% 0.54/0.76  (step t3.t2.t83 (cl (= (tptp.xor tptp.y tptp.falsehood) tptp.y)) :rule symm :premises (t3.t2.a4))
% 0.54/0.76  (step t3.t2.t84 (cl (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) tptp.y)) :rule trans :premises (t3.t2.t77 t3.t2.t80 t3.t2.t81 t3.t2.t82 t3.t2.t83))
% 0.54/0.76  (step t3.t2.t85 (cl (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.truth tptp.x))) :rule refl)
% 0.54/0.76  (step t3.t2.t86 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) :rule cong :premises (t3.t2.t84 t3.t2.t85))
% 0.54/0.76  (step t3.t2.t87 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule trans :premises (t3.t2.t86 t3.t2.a3))
% 0.54/0.76  (step t3.t2.t88 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y) tptp.truth))) :rule cong :premises (t3.t2.t87 t3.t2.t9))
% 0.54/0.76  (step t3.t2.t89 (cl (= (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y) (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) :rule symm :premises (t3.t2.a3))
% 0.54/0.76  (step t3.t2.t90 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y) tptp.truth) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule cong :premises (t3.t2.t89 t3.t2.t9))
% 0.54/0.76  (step t3.t2.t91 (cl (= (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule symm :premises (t3.t2.a2))
% 0.54/0.76  (step t3.t2.t92 (cl (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.implies tptp.y tptp.x))) :rule symm :premises (t3.t2.a1))
% 0.54/0.76  (step t3.t2.t93 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.implies tptp.y tptp.x))) :rule trans :premises (t3.t2.t88 t3.t2.t90 t3.t2.t91 t3.t2.t92))
% 0.54/0.76  (step t3.t2.t94 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) :rule cong :premises (t3.t2.t93 t3.t2.t85))
% 0.54/0.76  (step t3.t2.t95 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) :rule trans :premises (t3.t2.t54 t3.t2.t55 t3.t2.t56 t3.t2.t74 t3.t2.t75 t3.t2.t94))
% 0.54/0.76  (step t3.t2.t96 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule cong :premises (t3.t2.t9 t3.t2.t95))
% 0.54/0.76  (step t3.t2.t97 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule symm :premises (t3.t2.a0))
% 0.54/0.76  (step t3.t2.t98 (cl (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule trans :premises (t3.t2.t50 t3.t2.t52 t3.t2.t96 t3.t2.t97))
% 0.54/0.76  (step t3.t2 (cl (not (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (not (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (not (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (not (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (not (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (not (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (not (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (not (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (not (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (not (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :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))
% 0.54/0.76  (step t3.t3 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule and_pos)
% 0.54/0.76  (step t3.t4 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule and_pos)
% 0.54/0.76  (step t3.t5 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t6 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule and_pos)
% 0.54/0.76  (step t3.t7 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule and_pos)
% 0.54/0.76  (step t3.t8 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= tptp.falsehood (tptp.not tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t9 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t10 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t11 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t12 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t13 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule and_pos)
% 0.54/0.76  (step t3.t14 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t15 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t16 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t17 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule and_pos)
% 0.54/0.76  (step t3.t18 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule and_pos)
% 0.54/0.76  (step t3.t19 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t20 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t3.t21 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule and_pos)
% 0.54/0.76  (step t3.t22 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t3.t23 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t24 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule and_pos)
% 0.54/0.76  (step t3.t25 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule and_pos)
% 0.54/0.76  (step t3.t26 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule and_pos)
% 0.54/0.76  (step t3.t27 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t3.t28 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule and_pos)
% 0.54/0.76  (step t3.t29 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t3.t30 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule and_pos)
% 0.54/0.76  (step t3.t31 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule and_pos)
% 0.54/0.76  (step t3.t32 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule and_pos)
% 0.54/0.76  (step t3.t33 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t3.t34 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t3.t35 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t3.t36 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule and_pos)
% 0.54/0.76  (step t3.t37 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t3.t38 (cl (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))))) :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))
% 0.54/0.76  (step t3.t39 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule reordering :premises (t3.t38))
% 0.54/0.76  (step t3.t40 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule contraction :premises (t3.t39))
% 0.54/0.76  (step t3.t41 (cl (=> (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule resolution :premises (t3.t1 t3.t40))
% 0.54/0.76  (step t3.t42 (cl (=> (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (not (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)))) :rule implies_neg2)
% 0.54/0.76  (step t3.t43 (cl (=> (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (=> (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)))) :rule resolution :premises (t3.t41 t3.t42))
% 0.54/0.76  (step t3.t44 (cl (=> (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)))) :rule contraction :premises (t3.t43))
% 0.54/0.76  (step t3.t45 (cl (not (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule implies :premises (t3.t44))
% 0.54/0.76  (step t3.t46 (cl (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (not (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (not (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (not (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (not (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (not (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (not (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (not (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (not (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (not (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :rule and_neg)
% 0.54/0.76  (step t3.t47 (cl (and (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t3.t46 t3.a4 t3.a3 t3.a9 t3.a12 t3.a31 t3.a0 t3.a1 t3.a22 t3.a7 t3.a16 t3.a34 t3.a17 t3.a6 t3.a23 t3.a30 t3.a11 t3.a8 t3.a2 t3.a13 t3.a14 t3.a32 t3.a29 t3.a33 t3.a15 t3.a26 t3.a24 t3.a19 t3.a18 t3.a25 t3.a20 t3.a5 t3.a10 t3.a21 t3.a27 t3.a28))
% 0.54/0.76  (step t3.t48 (cl (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule resolution :premises (t3.t45 t3.t47))
% 0.54/0.76  (step t3 (cl (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (not (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (not (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (not (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (not (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (not (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (not (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (not (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :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))
% 0.54/0.76  (step t4 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= tptp.falsehood (tptp.not tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t5 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t6 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t7 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule and_pos)
% 0.54/0.76  (step t8 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule and_pos)
% 0.54/0.76  (step t9 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t10 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t11 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t12 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t13 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t14 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t15 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule and_pos)
% 0.54/0.76  (step t16 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule and_pos)
% 0.54/0.76  (step t17 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule and_pos)
% 0.54/0.76  (step t18 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t19 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule and_pos)
% 0.54/0.76  (step t20 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t21 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t22 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule and_pos)
% 0.54/0.76  (step t23 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t24 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule and_pos)
% 0.54/0.76  (step t25 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.76  (step t26 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t27 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule and_pos)
% 0.54/0.76  (step t28 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule and_pos)
% 0.54/0.76  (step t29 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule and_pos)
% 0.54/0.77  (step t30 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.77  (step t31 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule and_pos)
% 0.54/0.77  (step t32 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule and_pos)
% 0.54/0.77  (step t33 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule and_pos)
% 0.54/0.77  (step t34 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule and_pos)
% 0.54/0.77  (step t35 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule and_pos)
% 0.54/0.77  (step t36 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule and_pos)
% 0.54/0.77  (step t37 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule and_pos)
% 0.54/0.77  (step t38 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule and_pos)
% 0.54/0.77  (step t39 (cl (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :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))
% 0.54/0.77  (step t40 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule reordering :premises (t39))
% 0.54/0.77  (step t41 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule contraction :premises (t40))
% 0.54/0.77  (step t42 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule resolution :premises (t2 t41))
% 0.54/0.77  (step t43 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (not (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)))) :rule implies_neg2)
% 0.54/0.77  (step t44 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)))) :rule resolution :premises (t42 t43))
% 0.54/0.77  (step t45 (cl (=> (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)))) :rule contraction :premises (t44))
% 0.54/0.77  (step t46 (cl (not (and (= tptp.falsehood (tptp.not tptp.truth)) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)) (= tptp.x (tptp.xor tptp.x tptp.falsehood)) (= tptp.y (tptp.xor tptp.y tptp.falsehood)) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule implies :premises (t45))
% 0.54/0.77  (step t47 (cl (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (not (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (not (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (not (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (not (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (not (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (not (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (not (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x))) :rule resolution :premises (t1 t46))
% 0.54/0.77  (step t48 (cl (= (tptp.implies (tptp.implies tptp.x tptp.y) tptp.y) (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x)) (not (= tptp.falsehood (tptp.not tptp.truth))) (not (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (not (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (not (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (not (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (not (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (not (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (not (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (not (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule reordering :premises (t47))
% 0.54/0.77  (step t49 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t50)
% 0.54/0.77  (assume t50.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))))
% 0.54/0.77  (step t50.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule forall_inst :args ((:= X (tptp.xor tptp.truth tptp.y)) (:= Y (tptp.xor tptp.truth tptp.x))))
% 0.54/0.77  (step t50.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule or :premises (t50.t1))
% 0.54/0.77  (step t50.t3 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule resolution :premises (t50.t2 t50.a0))
% 0.54/0.77  (step t50 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule subproof :discharge (t50.a0))
% 0.54/0.77  (step t51 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule resolution :premises (t49 t50))
% 0.54/0.77  (step t52 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule implies_neg2)
% 0.54/0.77  (step t53 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t51 t52))
% 0.54/0.77  (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule contraction :premises (t53))
% 0.54/0.77  (step t55 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule implies :premises (t54))
% 0.54/0.77  (step t56 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.x)) tptp.truth) (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))) :rule resolution :premises (t55 a7))
% 0.54/0.77  (step t57 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t58)
% 0.54/0.77  (assume t58.a0 (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))))
% 0.54/0.77  (step t58.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.x)))
% 0.54/0.77  (step t58.t2 (cl (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule or :premises (t58.t1))
% 0.54/0.77  (step t58.t3 (cl (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule resolution :premises (t58.t2 t58.a0))
% 0.54/0.77  (step t58 (cl (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule subproof :discharge (t58.a0))
% 0.54/0.77  (step t59 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule resolution :premises (t57 t58))
% 0.54/0.77  (step t60 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (not (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule implies_neg2)
% 0.54/0.77  (step t61 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule resolution :premises (t59 t60))
% 0.54/0.77  (step t62 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood)))) :rule contraction :premises (t61))
% 0.54/0.77  (step t63 (cl (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule implies :premises (t62))
% 0.54/0.77  (step t64 (cl (not (= (forall ((X $$unsorted)) (= (tptp.and_star X tptp.falsehood) tptp.falsehood)) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))))) (not (forall ((X $$unsorted)) (= (tptp.and_star X tptp.falsehood) tptp.falsehood))) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) :rule equiv_pos2)
% 0.54/0.77  (anchor :step t65 :args ((X $$unsorted) (:= X X)))
% 0.54/0.77  (step t65.t1 (cl (= X X)) :rule refl)
% 0.54/0.77  (step t65.t2 (cl (= (= (tptp.and_star X tptp.falsehood) tptp.falsehood) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) :rule all_simplify)
% 0.54/0.77  (step t65 (cl (= (forall ((X $$unsorted)) (= (tptp.and_star X tptp.falsehood) tptp.falsehood)) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood))))) :rule bind)
% 0.54/0.77  (step t66 (cl (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star X tptp.falsehood)))) :rule resolution :premises (t64 t65 a4))
% 0.54/0.77  (step t67 (cl (= tptp.falsehood (tptp.and_star tptp.x tptp.falsehood))) :rule resolution :premises (t63 t66))
% 0.54/0.77  (step t68 (cl (=> (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t69)
% 0.54/0.77  (assume t69.a0 (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))))
% 0.54/0.77  (step t69.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule forall_inst :args ((:= X (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t69.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule or :premises (t69.t1))
% 0.54/0.77  (step t69.t3 (cl (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule resolution :premises (t69.t2 t69.a0))
% 0.54/0.77  (step t69 (cl (not (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule subproof :discharge (t69.a0))
% 0.54/0.77  (step t70 (cl (=> (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule resolution :premises (t68 t69))
% 0.54/0.77  (step t71 (cl (=> (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t72 (cl (=> (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) (=> (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule resolution :premises (t70 t71))
% 0.54/0.77  (step t73 (cl (=> (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule contraction :premises (t72))
% 0.54/0.77  (step t74 (cl (not (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth)))) (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule implies :premises (t73))
% 0.54/0.77  (step t75 (cl (not (= (forall ((X $$unsorted)) (= (tptp.and_star X tptp.truth) X)) (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))))) (not (forall ((X $$unsorted)) (= (tptp.and_star X tptp.truth) X))) (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth)))) :rule equiv_pos2)
% 0.54/0.77  (anchor :step t76 :args ((X $$unsorted) (:= X X)))
% 0.54/0.77  (step t76.t1 (cl (= X X)) :rule refl)
% 0.54/0.77  (step t76.t2 (cl (= (= (tptp.and_star X tptp.truth) X) (= X (tptp.and_star X tptp.truth)))) :rule all_simplify)
% 0.54/0.77  (step t76 (cl (= (forall ((X $$unsorted)) (= (tptp.and_star X tptp.truth) X)) (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth))))) :rule bind)
% 0.54/0.77  (step t77 (cl (forall ((X $$unsorted)) (= X (tptp.and_star X tptp.truth)))) :rule resolution :premises (t75 t76 a3))
% 0.54/0.77  (step t78 (cl (= (tptp.xor tptp.truth tptp.y) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule resolution :premises (t74 t77))
% 0.54/0.77  (step t79 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t80)
% 0.54/0.77  (assume t80.a0 (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))))
% 0.54/0.77  (step t80.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.y (tptp.xor tptp.y tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.y)))
% 0.54/0.77  (step t80.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule or :premises (t80.t1))
% 0.54/0.77  (step t80.t3 (cl (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule resolution :premises (t80.t2 t80.a0))
% 0.54/0.77  (step t80 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule subproof :discharge (t80.a0))
% 0.54/0.77  (step t81 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule resolution :premises (t79 t80))
% 0.54/0.77  (step t82 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (not (= tptp.y (tptp.xor tptp.y tptp.falsehood)))) :rule implies_neg2)
% 0.54/0.77  (step t83 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.y (tptp.xor tptp.y tptp.falsehood)))) :rule resolution :premises (t81 t82))
% 0.54/0.77  (step t84 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.y (tptp.xor tptp.y tptp.falsehood)))) :rule contraction :premises (t83))
% 0.54/0.77  (step t85 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule implies :premises (t84))
% 0.54/0.77  (step t86 (cl (not (= (forall ((X $$unsorted)) (= (tptp.xor X tptp.falsehood) X)) (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))))) (not (forall ((X $$unsorted)) (= (tptp.xor X tptp.falsehood) X))) (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) :rule equiv_pos2)
% 0.54/0.77  (anchor :step t87 :args ((X $$unsorted) (:= X X)))
% 0.54/0.77  (step t87.t1 (cl (= X X)) :rule refl)
% 0.54/0.77  (step t87.t2 (cl (= (= (tptp.xor X tptp.falsehood) X) (= X (tptp.xor X tptp.falsehood)))) :rule all_simplify)
% 0.54/0.77  (step t87 (cl (= (forall ((X $$unsorted)) (= (tptp.xor X tptp.falsehood) X)) (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))))) :rule bind)
% 0.54/0.77  (step t88 (cl (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) :rule resolution :premises (t86 t87 a1))
% 0.54/0.77  (step t89 (cl (= tptp.y (tptp.xor tptp.y tptp.falsehood))) :rule resolution :premises (t85 t88))
% 0.54/0.77  (step t90 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t91)
% 0.54/0.77  (assume t91.a0 (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))))
% 0.54/0.77  (step t91.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.x (tptp.xor tptp.x tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.x)))
% 0.54/0.77  (step t91.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule or :premises (t91.t1))
% 0.54/0.77  (step t91.t3 (cl (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule resolution :premises (t91.t2 t91.a0))
% 0.54/0.77  (step t91 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule subproof :discharge (t91.a0))
% 0.54/0.77  (step t92 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule resolution :premises (t90 t91))
% 0.54/0.77  (step t93 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (not (= tptp.x (tptp.xor tptp.x tptp.falsehood)))) :rule implies_neg2)
% 0.54/0.77  (step t94 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.x (tptp.xor tptp.x tptp.falsehood)))) :rule resolution :premises (t92 t93))
% 0.54/0.77  (step t95 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.x (tptp.xor tptp.x tptp.falsehood)))) :rule contraction :premises (t94))
% 0.54/0.77  (step t96 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule implies :premises (t95))
% 0.54/0.77  (step t97 (cl (= tptp.x (tptp.xor tptp.x tptp.falsehood))) :rule resolution :premises (t96 t88))
% 0.54/0.77  (step t98 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t99)
% 0.54/0.77  (assume t99.a0 (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))))
% 0.54/0.77  (step t99.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)))) :rule forall_inst :args ((:= X tptp.truth)))
% 0.54/0.77  (step t99.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule or :premises (t99.t1))
% 0.54/0.77  (step t99.t3 (cl (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule resolution :premises (t99.t2 t99.a0))
% 0.54/0.77  (step t99 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule subproof :discharge (t99.a0))
% 0.54/0.77  (step t100 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule resolution :premises (t98 t99))
% 0.54/0.77  (step t101 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (not (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)))) :rule implies_neg2)
% 0.54/0.77  (step t102 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)))) :rule resolution :premises (t100 t101))
% 0.54/0.77  (step t103 (cl (=> (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood)))) :rule contraction :premises (t102))
% 0.54/0.77  (step t104 (cl (not (forall ((X $$unsorted)) (= X (tptp.xor X tptp.falsehood)))) (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule implies :premises (t103))
% 0.54/0.77  (step t105 (cl (= tptp.truth (tptp.xor tptp.truth tptp.falsehood))) :rule resolution :premises (t104 t88))
% 0.54/0.77  (step t106 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t107)
% 0.54/0.77  (assume t107.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))))
% 0.54/0.77  (step t107.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :rule forall_inst :args ((:= X (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (:= Y tptp.y)))
% 0.54/0.77  (step t107.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule or :premises (t107.t1))
% 0.54/0.77  (step t107.t3 (cl (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t107.t2 t107.a0))
% 0.54/0.77  (step t107 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule subproof :discharge (t107.a0))
% 0.54/0.77  (step t108 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t106 t107))
% 0.54/0.77  (step t109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :rule implies_neg2)
% 0.54/0.77  (step t110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t108 t109))
% 0.54/0.77  (step t111 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)))))) :rule contraction :premises (t110))
% 0.54/0.77  (step t112 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule implies :premises (t111))
% 0.54/0.77  (step t113 (cl (= (tptp.implies (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) tptp.y) (tptp.xor tptp.truth (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t112 a12))
% 0.54/0.77  (step t114 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t115)
% 0.54/0.77  (assume t115.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.77  (step t115.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))))) :rule forall_inst :args ((:= X (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (:= Y (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t115.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule or :premises (t115.t1))
% 0.54/0.77  (step t115.t3 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule resolution :premises (t115.t2 t115.a0))
% 0.54/0.77  (step t115 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule subproof :discharge (t115.a0))
% 0.54/0.77  (step t116 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule resolution :premises (t114 t115))
% 0.54/0.77  (step t117 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))))) :rule implies_neg2)
% 0.54/0.77  (step t118 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))))) :rule resolution :premises (t116 t117))
% 0.54/0.77  (step t119 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))))) :rule contraction :premises (t118))
% 0.54/0.77  (step t120 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule implies :premises (t119))
% 0.54/0.77  (step t121 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule resolution :premises (t120 a10))
% 0.54/0.77  (step t122 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t123)
% 0.54/0.77  (assume t123.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.77  (step t123.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule forall_inst :args ((:= X (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (:= Y (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t123.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule or :premises (t123.t1))
% 0.54/0.77  (step t123.t3 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t123.t2 t123.a0))
% 0.54/0.77  (step t123 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule subproof :discharge (t123.a0))
% 0.54/0.77  (step t124 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t122 t123))
% 0.54/0.77  (step t125 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule implies_neg2)
% 0.54/0.77  (step t126 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t124 t125))
% 0.54/0.77  (step t127 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule contraction :premises (t126))
% 0.54/0.77  (step t128 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule implies :premises (t127))
% 0.54/0.77  (step t129 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t128 a10))
% 0.54/0.77  (step t130 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t131)
% 0.54/0.77  (assume t131.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))))
% 0.54/0.77  (step t131.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.xor tptp.truth tptp.y)) (:= Z (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))
% 0.54/0.77  (step t131.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule or :premises (t131.t1))
% 0.54/0.77  (step t131.t3 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule resolution :premises (t131.t2 t131.a0))
% 0.54/0.77  (step t131 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule subproof :discharge (t131.a0))
% 0.54/0.77  (step t132 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule resolution :premises (t130 t131))
% 0.54/0.77  (step t133 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))))) :rule implies_neg2)
% 0.54/0.77  (step t134 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))))) :rule resolution :premises (t132 t133))
% 0.54/0.77  (step t135 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))))) :rule contraction :premises (t134))
% 0.54/0.77  (step t136 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule implies :premises (t135))
% 0.54/0.77  (step t137 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule resolution :premises (t136 a9))
% 0.54/0.77  (step t138 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t139)
% 0.54/0.77  (assume t139.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))))
% 0.54/0.77  (step t139.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.xor tptp.truth tptp.y)) (:= Z (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.77  (step t139.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule or :premises (t139.t1))
% 0.54/0.77  (step t139.t3 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t139.t2 t139.a0))
% 0.54/0.77  (step t139 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule subproof :discharge (t139.a0))
% 0.54/0.77  (step t140 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t138 t139))
% 0.54/0.77  (step t141 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))))) :rule implies_neg2)
% 0.54/0.77  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))))) :rule resolution :premises (t140 t141))
% 0.54/0.77  (step t143 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z)))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))))) :rule contraction :premises (t142))
% 0.54/0.77  (step t144 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.and_star (tptp.and_star X Y) Z) (tptp.and_star X (tptp.and_star Y Z))))) (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule implies :premises (t143))
% 0.54/0.77  (step t145 (cl (= (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (tptp.and_star tptp.x (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t144 a9))
% 0.54/0.77  (step t146 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t147)
% 0.54/0.77  (assume t147.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))))
% 0.54/0.77  (step t147.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.truth)))
% 0.54/0.77  (step t147.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule or :premises (t147.t1))
% 0.54/0.77  (step t147.t3 (cl (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule resolution :premises (t147.t2 t147.a0))
% 0.54/0.77  (step t147 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule subproof :discharge (t147.a0))
% 0.54/0.77  (step t148 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule resolution :premises (t146 t147))
% 0.54/0.77  (step t149 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t150 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)))) :rule resolution :premises (t148 t149))
% 0.54/0.77  (step t151 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth)))) :rule contraction :premises (t150))
% 0.54/0.77  (step t152 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule implies :premises (t151))
% 0.54/0.77  (step t153 (cl (= (tptp.xor tptp.x (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.x tptp.truth) tptp.truth))) :rule resolution :premises (t152 a6))
% 0.54/0.77  (step t154 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t155)
% 0.54/0.77  (assume t155.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))))
% 0.54/0.77  (step t155.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)))) :rule forall_inst :args ((:= X tptp.y) (:= Y tptp.truth)))
% 0.54/0.77  (step t155.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule or :premises (t155.t1))
% 0.54/0.77  (step t155.t3 (cl (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule resolution :premises (t155.t2 t155.a0))
% 0.54/0.77  (step t155 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule subproof :discharge (t155.a0))
% 0.54/0.77  (step t156 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule resolution :premises (t154 t155))
% 0.54/0.77  (step t157 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (not (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t158 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)))) :rule resolution :premises (t156 t157))
% 0.54/0.77  (step t159 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth)))) :rule contraction :premises (t158))
% 0.54/0.77  (step t160 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X (tptp.xor tptp.truth Y)) (tptp.xor (tptp.xor X tptp.truth) Y)))) (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule implies :premises (t159))
% 0.54/0.77  (step t161 (cl (= (tptp.xor tptp.y (tptp.xor tptp.truth tptp.truth)) (tptp.xor (tptp.xor tptp.y tptp.truth) tptp.truth))) :rule resolution :premises (t160 a6))
% 0.54/0.77  (step t162 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))))) (not (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))))) :rule equiv_pos2)
% 0.54/0.77  (step t163 (cl (= (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))))) :rule refl)
% 0.54/0.77  (step t164 (cl (= (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))))) :rule all_simplify)
% 0.54/0.77  (step t165 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))))) :rule cong :premises (t163 t164))
% 0.54/0.77  (step t166 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t167)
% 0.54/0.77  (assume t167.a0 (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))))
% 0.54/0.77  (step t167.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule forall_inst :args ((:= X (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.77  (step t167.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule or :premises (t167.t1))
% 0.54/0.77  (step t167.t3 (cl (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t167.t2 t167.a0))
% 0.54/0.77  (step t167 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule subproof :discharge (t167.a0))
% 0.54/0.77  (step t168 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t166 t167))
% 0.54/0.77  (step t169 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t170 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule resolution :premises (t168 t169))
% 0.54/0.77  (step t171 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule contraction :premises (t170))
% 0.54/0.77  (step t172 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t162 t165 t171))
% 0.54/0.77  (step t173 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) :rule implies :premises (t172))
% 0.54/0.77  (step t174 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t173 a0))
% 0.54/0.77  (step t175 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t176)
% 0.54/0.77  (assume t176.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.77  (step t176.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule forall_inst :args ((:= X (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)) (:= Y (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.77  (step t176.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule or :premises (t176.t1))
% 0.54/0.77  (step t176.t3 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule resolution :premises (t176.t2 t176.a0))
% 0.54/0.77  (step t176 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule subproof :discharge (t176.a0))
% 0.54/0.77  (step t177 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule resolution :premises (t175 t176))
% 0.54/0.77  (step t178 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule implies_neg2)
% 0.54/0.77  (step t179 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule resolution :premises (t177 t178))
% 0.54/0.77  (step t180 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth))))) :rule contraction :premises (t179))
% 0.54/0.77  (step t181 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule implies :premises (t180))
% 0.54/0.77  (step t182 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth)))) :rule resolution :premises (t181 a10))
% 0.54/0.77  (step t183 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t184)
% 0.54/0.77  (assume t184.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.77  (step t184.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule forall_inst :args ((:= X (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))) (:= Y (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.77  (step t184.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule or :premises (t184.t1))
% 0.54/0.77  (step t184.t3 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t184.t2 t184.a0))
% 0.54/0.77  (step t184 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule subproof :discharge (t184.a0))
% 0.54/0.77  (step t185 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t183 t184))
% 0.54/0.77  (step t186 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule implies_neg2)
% 0.54/0.77  (step t187 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t185 t186))
% 0.54/0.77  (step t188 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)))))) :rule contraction :premises (t187))
% 0.54/0.77  (step t189 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule implies :premises (t188))
% 0.54/0.77  (step t190 (cl (= (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.and_star (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t189 a10))
% 0.54/0.77  (step t191 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t192)
% 0.54/0.77  (assume t192.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t192.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))) :rule forall_inst :args ((:= X (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))) (:= Y tptp.truth)))
% 0.54/0.77  (step t192.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule or :premises (t192.t1))
% 0.54/0.77  (step t192.t3 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t192.t2 t192.a0))
% 0.54/0.77  (step t192 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule subproof :discharge (t192.a0))
% 0.54/0.77  (step t193 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t191 t192))
% 0.54/0.77  (step t194 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (not (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))) :rule implies_neg2)
% 0.54/0.77  (step t195 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))) :rule resolution :premises (t193 t194))
% 0.54/0.77  (step t196 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))) :rule contraction :premises (t195))
% 0.54/0.77  (step t197 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule implies :premises (t196))
% 0.54/0.77  (step t198 (cl (= (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.xor tptp.truth (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t197 a8))
% 0.54/0.77  (step t199 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t200)
% 0.54/0.77  (assume t200.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t200.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.xor tptp.truth tptp.x))))
% 0.54/0.77  (step t200.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule or :premises (t200.t1))
% 0.54/0.77  (step t200.t3 (cl (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule resolution :premises (t200.t2 t200.a0))
% 0.54/0.77  (step t200 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule subproof :discharge (t200.a0))
% 0.54/0.77  (step t201 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule resolution :premises (t199 t200))
% 0.54/0.77  (step t202 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t203 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)))) :rule resolution :premises (t201 t202))
% 0.54/0.77  (step t204 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth)))) :rule contraction :premises (t203))
% 0.54/0.77  (step t205 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule implies :premises (t204))
% 0.54/0.77  (step t206 (cl (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.x)) (tptp.xor (tptp.xor tptp.truth tptp.x) tptp.truth))) :rule resolution :premises (t205 a8))
% 0.54/0.77  (step t207 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t208)
% 0.54/0.77  (assume t208.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t208.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t208.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule or :premises (t208.t1))
% 0.54/0.77  (step t208.t3 (cl (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule resolution :premises (t208.t2 t208.a0))
% 0.54/0.77  (step t208 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule subproof :discharge (t208.a0))
% 0.54/0.77  (step t209 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule resolution :premises (t207 t208))
% 0.54/0.77  (step t210 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t211 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule resolution :premises (t209 t210))
% 0.54/0.77  (step t212 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth)))) :rule contraction :premises (t211))
% 0.54/0.77  (step t213 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule implies :premises (t212))
% 0.54/0.77  (step t214 (cl (= (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor (tptp.xor tptp.truth tptp.y) tptp.truth))) :rule resolution :premises (t213 a8))
% 0.54/0.77  (step t215 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t216)
% 0.54/0.77  (assume t216.a0 (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))))
% 0.54/0.77  (step t216.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))))) :rule forall_inst :args ((:= X (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t216.t2 (cl (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule or :premises (t216.t1))
% 0.54/0.77  (step t216.t3 (cl (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule resolution :premises (t216.t2 t216.a0))
% 0.54/0.77  (step t216 (cl (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule subproof :discharge (t216.a0))
% 0.54/0.77  (step t217 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule resolution :premises (t215 t216))
% 0.54/0.77  (step t218 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (not (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))))) :rule implies_neg2)
% 0.54/0.77  (step t219 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t217 t218))
% 0.54/0.77  (step t220 (cl (=> (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y))))) :rule contraction :premises (t219))
% 0.54/0.77  (step t221 (cl (not (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule implies :premises (t220))
% 0.54/0.77  (step t222 (cl (not (= (forall ((X $$unsorted)) (= (tptp.and_star (tptp.xor tptp.truth X) X) tptp.falsehood)) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))))) (not (forall ((X $$unsorted)) (= (tptp.and_star (tptp.xor tptp.truth X) X) tptp.falsehood))) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) :rule equiv_pos2)
% 0.54/0.77  (anchor :step t223 :args ((X $$unsorted) (:= X X)))
% 0.54/0.77  (step t223.t1 (cl (= X X)) :rule refl)
% 0.54/0.77  (step t223.t2 (cl (= (= (tptp.and_star (tptp.xor tptp.truth X) X) tptp.falsehood) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) :rule all_simplify)
% 0.54/0.77  (step t223 (cl (= (forall ((X $$unsorted)) (= (tptp.and_star (tptp.xor tptp.truth X) X) tptp.falsehood)) (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X))))) :rule bind)
% 0.54/0.77  (step t224 (cl (forall ((X $$unsorted)) (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth X) X)))) :rule resolution :premises (t222 t223 a5))
% 0.54/0.77  (step t225 (cl (= tptp.falsehood (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.xor tptp.truth tptp.y)))) :rule resolution :premises (t221 t224))
% 0.54/0.77  (step t226 (cl (not (= (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))) (not (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule equiv_pos2)
% 0.54/0.77  (step t227 (cl (= (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule all_simplify)
% 0.54/0.77  (step t228 (cl (= (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))))) :rule cong :premises (t163 t227))
% 0.54/0.77  (step t229 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t230)
% 0.54/0.77  (assume t230.a0 (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))))
% 0.54/0.77  (step t230.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule forall_inst :args ((:= X (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.77  (step t230.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule or :premises (t230.t1))
% 0.54/0.77  (step t230.t3 (cl (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t230.t2 t230.a0))
% 0.54/0.77  (step t230 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule subproof :discharge (t230.a0))
% 0.54/0.77  (step t231 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t229 t230))
% 0.54/0.77  (step t232 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t233 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule resolution :premises (t231 t232))
% 0.54/0.77  (step t234 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule contraction :premises (t233))
% 0.54/0.77  (step t235 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t226 t228 t234))
% 0.54/0.77  (step t236 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule implies :premises (t235))
% 0.54/0.77  (step t237 (cl (= (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.not (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t236 a0))
% 0.54/0.77  (step t238 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t239)
% 0.54/0.77  (assume t239.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.77  (step t239.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))))) :rule forall_inst :args ((:= X (tptp.implies tptp.x tptp.y)) (:= Y (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t239.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule or :premises (t239.t1))
% 0.54/0.77  (step t239.t3 (cl (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule resolution :premises (t239.t2 t239.a0))
% 0.54/0.77  (step t239 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule subproof :discharge (t239.a0))
% 0.54/0.77  (step t240 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule resolution :premises (t238 t239))
% 0.54/0.77  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (not (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))))) :rule implies_neg2)
% 0.54/0.77  (step t242 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))))) :rule resolution :premises (t240 t241))
% 0.54/0.77  (step t243 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y))))) :rule contraction :premises (t242))
% 0.54/0.77  (step t244 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule implies :premises (t243))
% 0.54/0.77  (step t245 (cl (= (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) (tptp.implies tptp.x tptp.y)))) :rule resolution :premises (t244 a10))
% 0.54/0.77  (step t246 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t247)
% 0.54/0.77  (assume t247.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.77  (step t247.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)))) :rule forall_inst :args ((:= X tptp.y) (:= Y (tptp.xor tptp.truth tptp.x))))
% 0.54/0.77  (step t247.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule or :premises (t247.t1))
% 0.54/0.77  (step t247.t3 (cl (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule resolution :premises (t247.t2 t247.a0))
% 0.54/0.77  (step t247 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule subproof :discharge (t247.a0))
% 0.54/0.77  (step t248 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule resolution :premises (t246 t247))
% 0.54/0.77  (step t249 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (not (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)))) :rule implies_neg2)
% 0.54/0.77  (step t250 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)))) :rule resolution :premises (t248 t249))
% 0.54/0.77  (step t251 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y)))) :rule contraction :premises (t250))
% 0.54/0.77  (step t252 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule implies :premises (t251))
% 0.54/0.77  (step t253 (cl (= (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) (tptp.and_star (tptp.xor tptp.truth tptp.x) tptp.y))) :rule resolution :premises (t252 a10))
% 0.54/0.77  (step t254 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t255)
% 0.54/0.77  (assume t255.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))))
% 0.54/0.77  (step t255.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)))) :rule forall_inst :args ((:= X tptp.x) (:= Y (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t255.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule or :premises (t255.t1))
% 0.54/0.77  (step t255.t3 (cl (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule resolution :premises (t255.t2 t255.a0))
% 0.54/0.77  (step t255 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule subproof :discharge (t255.a0))
% 0.54/0.77  (step t256 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule resolution :premises (t254 t255))
% 0.54/0.77  (step t257 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (not (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)))) :rule implies_neg2)
% 0.54/0.77  (step t258 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)))) :rule resolution :premises (t256 t257))
% 0.54/0.77  (step t259 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x)))) :rule contraction :premises (t258))
% 0.54/0.77  (step t260 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star X Y) (tptp.and_star Y X)))) (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule implies :premises (t259))
% 0.54/0.77  (step t261 (cl (= (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor tptp.truth tptp.y) tptp.x))) :rule resolution :premises (t260 a10))
% 0.54/0.77  (step t262 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t263)
% 0.54/0.77  (assume t263.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t263.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.77  (step t263.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule or :premises (t263.t1))
% 0.54/0.77  (step t263.t3 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t263.t2 t263.a0))
% 0.54/0.77  (step t263 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule subproof :discharge (t263.a0))
% 0.54/0.77  (step t264 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t262 t263))
% 0.54/0.77  (step t265 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t266 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule resolution :premises (t264 t265))
% 0.54/0.77  (step t267 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule contraction :premises (t266))
% 0.54/0.77  (step t268 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule implies :premises (t267))
% 0.54/0.77  (step t269 (cl (= (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t268 a8))
% 0.54/0.77  (step t270 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t271)
% 0.54/0.77  (assume t271.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t271.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))))
% 0.54/0.77  (step t271.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule or :premises (t271.t1))
% 0.54/0.77  (step t271.t3 (cl (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule resolution :premises (t271.t2 t271.a0))
% 0.54/0.77  (step t271 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule subproof :discharge (t271.a0))
% 0.54/0.77  (step t272 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule resolution :premises (t270 t271))
% 0.54/0.77  (step t273 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t274 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)))) :rule resolution :premises (t272 t273))
% 0.54/0.77  (step t275 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth)))) :rule contraction :premises (t274))
% 0.54/0.77  (step t276 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule implies :premises (t275))
% 0.54/0.77  (step t277 (cl (= (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))) (tptp.xor (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)) tptp.truth))) :rule resolution :premises (t276 a8))
% 0.54/0.77  (step t278 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t279)
% 0.54/0.77  (assume t279.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t279.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))
% 0.54/0.77  (step t279.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule or :premises (t279.t1))
% 0.54/0.77  (step t279.t3 (cl (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t279.t2 t279.a0))
% 0.54/0.77  (step t279 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule subproof :discharge (t279.a0))
% 0.54/0.77  (step t280 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t278 t279))
% 0.54/0.77  (step t281 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (not (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t282 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule resolution :premises (t280 t281))
% 0.54/0.77  (step t283 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth)))) :rule contraction :premises (t282))
% 0.54/0.77  (step t284 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule implies :premises (t283))
% 0.54/0.77  (step t285 (cl (= (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)) tptp.truth))) :rule resolution :premises (t284 a8))
% 0.54/0.77  (step t286 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t287)
% 0.54/0.77  (assume t287.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t287.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y tptp.y)))
% 0.54/0.77  (step t287.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule or :premises (t287.t1))
% 0.54/0.77  (step t287.t3 (cl (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule resolution :premises (t287.t2 t287.a0))
% 0.54/0.77  (step t287 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule subproof :discharge (t287.a0))
% 0.54/0.77  (step t288 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule resolution :premises (t286 t287))
% 0.54/0.77  (step t289 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (not (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t290 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)))) :rule resolution :premises (t288 t289))
% 0.54/0.77  (step t291 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth)))) :rule contraction :premises (t290))
% 0.54/0.77  (step t292 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule implies :premises (t291))
% 0.54/0.77  (step t293 (cl (= (tptp.xor tptp.truth tptp.y) (tptp.xor tptp.y tptp.truth))) :rule resolution :premises (t292 a8))
% 0.54/0.77  (step t294 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t295)
% 0.54/0.77  (assume t295.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))))
% 0.54/0.77  (step t295.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth) (:= Y tptp.x)))
% 0.54/0.77  (step t295.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule or :premises (t295.t1))
% 0.54/0.77  (step t295.t3 (cl (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule resolution :premises (t295.t2 t295.a0))
% 0.54/0.77  (step t295 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule subproof :discharge (t295.a0))
% 0.54/0.77  (step t296 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule resolution :premises (t294 t295))
% 0.54/0.77  (step t297 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (not (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t298 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)))) :rule resolution :premises (t296 t297))
% 0.54/0.77  (step t299 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth)))) :rule contraction :premises (t298))
% 0.54/0.77  (step t300 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.xor X Y) (tptp.xor Y X)))) (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule implies :premises (t299))
% 0.54/0.77  (step t301 (cl (= (tptp.xor tptp.truth tptp.x) (tptp.xor tptp.x tptp.truth))) :rule resolution :premises (t300 a8))
% 0.54/0.77  (step t302 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t303)
% 0.54/0.77  (assume t303.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))))
% 0.54/0.77  (step t303.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule forall_inst :args ((:= X (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (:= Y (tptp.xor tptp.truth tptp.y))))
% 0.54/0.77  (step t303.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule or :premises (t303.t1))
% 0.54/0.77  (step t303.t3 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t303.t2 t303.a0))
% 0.54/0.77  (step t303 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule subproof :discharge (t303.a0))
% 0.54/0.77  (step t304 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t302 t303))
% 0.54/0.77  (step t305 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule implies_neg2)
% 0.54/0.77  (step t306 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t304 t305))
% 0.54/0.77  (step t307 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule contraction :premises (t306))
% 0.54/0.77  (step t308 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth X) Y) tptp.truth) Y) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth Y) X) tptp.truth) X)))) (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule implies :premises (t307))
% 0.54/0.77  (step t309 (cl (= (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) (tptp.xor tptp.truth tptp.y)) tptp.truth) (tptp.xor tptp.truth tptp.y)) (tptp.and_star (tptp.xor (tptp.and_star (tptp.xor tptp.truth (tptp.xor tptp.truth tptp.y)) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))) tptp.truth) (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t308 a7))
% 0.54/0.77  (step t310 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t311)
% 0.54/0.77  (assume t311.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))))
% 0.54/0.77  (step t311.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.y tptp.x)) (:= Y tptp.x)))
% 0.54/0.77  (step t311.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule or :premises (t311.t1))
% 0.54/0.77  (step t311.t3 (cl (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule resolution :premises (t311.t2 t311.a0))
% 0.54/0.77  (step t311 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule subproof :discharge (t311.a0))
% 0.54/0.77  (step t312 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule resolution :premises (t310 t311))
% 0.54/0.77  (step t313 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))))) :rule implies_neg2)
% 0.54/0.77  (step t314 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))))) :rule resolution :premises (t312 t313))
% 0.54/0.77  (step t315 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x)))))) :rule contraction :premises (t314))
% 0.54/0.77  (step t316 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule implies :premises (t315))
% 0.54/0.77  (step t317 (cl (= (tptp.implies (tptp.implies tptp.y tptp.x) tptp.x) (tptp.xor tptp.truth (tptp.and_star (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth tptp.x))))) :rule resolution :premises (t316 a12))
% 0.54/0.77  (step t318 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t319)
% 0.54/0.77  (assume t319.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))))
% 0.54/0.77  (step t319.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))))) :rule forall_inst :args ((:= X tptp.y) (:= Y tptp.x)))
% 0.54/0.77  (step t319.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule or :premises (t319.t1))
% 0.54/0.77  (step t319.t3 (cl (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule resolution :premises (t319.t2 t319.a0))
% 0.54/0.77  (step t319 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule subproof :discharge (t319.a0))
% 0.54/0.77  (step t320 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule resolution :premises (t318 t319))
% 0.54/0.77  (step t321 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (not (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))))) :rule implies_neg2)
% 0.54/0.77  (step t322 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))))) :rule resolution :premises (t320 t321))
% 0.54/0.77  (step t323 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x)))))) :rule contraction :premises (t322))
% 0.54/0.77  (step t324 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule implies :premises (t323))
% 0.54/0.77  (step t325 (cl (= (tptp.implies tptp.y tptp.x) (tptp.xor tptp.truth (tptp.and_star tptp.y (tptp.xor tptp.truth tptp.x))))) :rule resolution :premises (t324 a12))
% 0.54/0.77  (step t326 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t327)
% 0.54/0.77  (assume t327.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))))
% 0.54/0.77  (step t327.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.y)))
% 0.54/0.77  (step t327.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule or :premises (t327.t1))
% 0.54/0.77  (step t327.t3 (cl (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t327.t2 t327.a0))
% 0.54/0.77  (step t327 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule subproof :discharge (t327.a0))
% 0.54/0.77  (step t328 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t326 t327))
% 0.54/0.77  (step t329 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (not (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule implies_neg2)
% 0.54/0.77  (step t330 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule resolution :premises (t328 t329))
% 0.54/0.77  (step t331 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y)))))) :rule contraction :premises (t330))
% 0.54/0.77  (step t332 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X Y) (tptp.xor tptp.truth (tptp.and_star X (tptp.xor tptp.truth Y)))))) (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule implies :premises (t331))
% 0.54/0.77  (step t333 (cl (= (tptp.implies tptp.x tptp.y) (tptp.xor tptp.truth (tptp.and_star tptp.x (tptp.xor tptp.truth tptp.y))))) :rule resolution :premises (t332 a12))
% 0.54/0.77  (step t334 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) :rule implies_neg1)
% 0.54/0.77  (anchor :step t335)
% 0.54/0.77  (assume t335.a0 (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))))
% 0.54/0.77  (step t335.t1 (cl (or (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)))) :rule forall_inst :args ((:= X tptp.truth)))
% 0.54/0.77  (step t335.t2 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule or :premises (t335.t1))
% 0.54/0.77  (step t335.t3 (cl (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule resolution :premises (t335.t2 t335.a0))
% 0.54/0.77  (step t335 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule subproof :discharge (t335.a0))
% 0.54/0.77  (step t336 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule resolution :premises (t334 t335))
% 0.54/0.77  (step t337 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (not (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)))) :rule implies_neg2)
% 0.54/0.77  (step t338 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)))) :rule resolution :premises (t336 t337))
% 0.54/0.77  (step t339 (cl (=> (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth)))) :rule contraction :premises (t338))
% 0.54/0.77  (step t340 (cl (not (forall ((X $$unsorted)) (= (tptp.not X) (tptp.xor X tptp.truth)))) (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule implies :premises (t339))
% 0.54/0.77  (step t341 (cl (= (tptp.not tptp.truth) (tptp.xor tptp.truth tptp.truth))) :rule resolution :premises (t340 a0))
% 0.54/0.77  (step t342 (cl (= tptp.falsehood (tptp.not tptp.truth))) :rule symm :premises (a11))
% 0.54/0.77  (step t343 (cl) :rule resolution :premises (t48 t56 t67 t78 t89 t97 t105 t113 t121 t129 t137 t145 t153 t161 t174 t182 t190 t198 t206 t214 t225 t237 t245 t253 t261 t269 t277 t285 t293 t301 t309 t317 t325 t333 t341 a13 t342))
% 0.54/0.77  
% 0.54/0.77  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.mCQRm8KXKT/cvc5---1.0.5_6830.smt2
% 0.54/0.77  % cvc5---1.0.5 exiting
% 0.54/0.78  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------