%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL109-10 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n010.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 17:24:25 EDT 2024

% Result   : Unsatisfiable 7.41s 7.61s
% Output   : Proof 7.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : LCL109-10 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 27 19:52:54 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 7.41/7.61  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.suICpS9uhI/cvc5---1.0.5_10465.smt2
% 7.41/7.61  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.suICpS9uhI/cvc5---1.0.5_10465.smt2
% 7.54/7.82  (assume a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.ifeq A A B C) B)))
% 7.54/7.82  (assume a1 (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X)))
% 7.54/7.82  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth)))
% 7.54/7.82  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.54/7.82  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X)) tptp.truth)))
% 7.54/7.82  (assume a5 (forall ((X $$unsorted)) (= (tptp.implies X X) tptp.truth)))
% 7.54/7.82  (assume a6 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y) Y)))
% 7.54/7.82  (assume a7 (forall ((X $$unsorted)) (= (tptp.implies X tptp.truth) tptp.truth)))
% 7.54/7.82  (assume a8 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X (tptp.implies Y X)) tptp.truth)))
% 7.54/7.82  (assume a9 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.ifeq (tptp.implies X Y) (tptp.implies Y Z) (tptp.implies X Z) tptp.truth) tptp.truth)))
% 7.54/7.82  (assume a10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))) tptp.truth)))
% 7.54/7.82  (assume a11 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.54/7.82  (assume a12 (forall ((X $$unsorted)) (= (tptp.implies X (tptp.not tptp.truth)) (tptp.not X))))
% 7.54/7.82  (assume a13 (forall ((X $$unsorted)) (= (tptp.not (tptp.not X)) X)))
% 7.54/7.82  (assume a14 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.not X) (tptp.not Y)) (tptp.implies Y X))))
% 7.54/7.82  (assume a15 (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.truth)))
% 7.54/7.82  (step t1 (cl (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b tptp.b))) (not (= tptp.truth (tptp.implies tptp.a tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (not (= tptp.a (tptp.implies tptp.truth tptp.a))) (not (= tptp.b (tptp.implies tptp.truth tptp.b))) (not (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (not (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule and_neg)
% 7.54/7.82  (step t2 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule implies_neg1)
% 7.54/7.82  (anchor :step t3)
% 7.54/7.82  (assume t3.a0 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))))
% 7.54/7.82  (assume t3.a1 (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))
% 7.54/7.82  (assume t3.a2 (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))
% 7.54/7.82  (assume t3.a3 (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.a4 (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.a5 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.a6 (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.a7 (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.a8 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.a9 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.a10 (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))
% 7.54/7.82  (assume t3.a11 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (assume t3.a12 (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.a13 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.a14 (= tptp.truth (tptp.implies tptp.b tptp.b)))
% 7.54/7.82  (assume t3.a15 (= tptp.truth (tptp.implies tptp.a tptp.a)))
% 7.54/7.82  (assume t3.a16 (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))))
% 7.54/7.82  (assume t3.a17 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.a18 (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.a19 (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.a20 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.a21 (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.a22 (= tptp.a (tptp.implies tptp.truth tptp.a)))
% 7.54/7.82  (assume t3.a23 (= tptp.b (tptp.implies tptp.truth tptp.b)))
% 7.54/7.82  (assume t3.a24 (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))))
% 7.54/7.82  (assume t3.a25 (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))))
% 7.54/7.82  (assume t3.a26 (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.a27 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.a28 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.a29 (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))
% 7.54/7.82  (assume t3.a30 (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.a31 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.a32 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.a33 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.a34 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.a35 (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.a36 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.a37 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.a38 (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)))
% 7.54/7.82  (assume t3.a39 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.a40 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (assume t3.a41 (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.a42 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.a43 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (assume t3.a44 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.a45 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.a46 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))))
% 7.54/7.82  (assume t3.a47 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.a48 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.a49 (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))))
% 7.54/7.82  (assume t3.a50 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.a51 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))))
% 7.54/7.82  (assume t3.a52 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.a53 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.a54 (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)))
% 7.54/7.82  (assume t3.a55 (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))))
% 7.54/7.82  (assume t3.a56 (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.a57 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.a58 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))))
% 7.54/7.82  (assume t3.a59 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (step t3.t1 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) :rule implies_neg1)
% 7.54/7.82  (anchor :step t3.t2)
% 7.54/7.82  (assume t3.t2.a0 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))))
% 7.54/7.82  (assume t3.t2.a1 (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.t2.a2 (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.t2.a3 (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))
% 7.54/7.82  (assume t3.t2.a4 (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))))
% 7.54/7.82  (assume t3.t2.a5 (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.t2.a6 (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.t2.a7 (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))))
% 7.54/7.82  (assume t3.t2.a8 (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))
% 7.54/7.82  (assume t3.t2.a9 (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))
% 7.54/7.82  (assume t3.t2.a10 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.t2.a11 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.t2.a12 (= tptp.truth (tptp.implies tptp.b tptp.b)))
% 7.54/7.82  (assume t3.t2.a13 (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.t2.a14 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.t2.a15 (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.t2.a16 (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.t2.a17 (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.t2.a18 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.t2.a19 (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.t2.a20 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.t2.a21 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))))
% 7.54/7.82  (assume t3.t2.a22 (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.54/7.82  (assume t3.t2.a23 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.t2.a24 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.t2.a25 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.t2.a26 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.t2.a27 (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.t2.a28 (= tptp.truth (tptp.implies tptp.a tptp.a)))
% 7.54/7.82  (assume t3.t2.a29 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.t2.a30 (= tptp.b (tptp.implies tptp.truth tptp.b)))
% 7.54/7.82  (assume t3.t2.a31 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.t2.a32 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (assume t3.t2.a33 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))))
% 7.54/7.82  (assume t3.t2.a34 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.t2.a35 (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))))
% 7.54/7.82  (assume t3.t2.a36 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.t2.a37 (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.t2.a38 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))))
% 7.54/7.82  (assume t3.t2.a39 (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))
% 7.54/7.82  (assume t3.t2.a40 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.t2.a41 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))
% 7.54/7.82  (assume t3.t2.a42 (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))))
% 7.54/7.82  (assume t3.t2.a43 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))))
% 7.54/7.82  (assume t3.t2.a44 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))))
% 7.54/7.82  (assume t3.t2.a45 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (assume t3.t2.a46 (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (assume t3.t2.a47 (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)))
% 7.54/7.82  (assume t3.t2.a48 (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)))
% 7.54/7.82  (assume t3.t2.a49 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.t2.a50 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.t2.a51 (= tptp.a (tptp.implies tptp.truth tptp.a)))
% 7.54/7.82  (assume t3.t2.a52 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.t2.a53 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.54/7.82  (assume t3.t2.a54 (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.t2.a55 (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))
% 7.54/7.82  (assume t3.t2.a56 (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.t2.a57 (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.54/7.82  (assume t3.t2.a58 (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))))
% 7.54/7.82  (assume t3.t2.a59 (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))
% 7.54/7.82  (step t3.t2.t1 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) tptp.truth)) :rule symm :premises (t3.t2.a59))
% 7.54/7.82  (step t3.t2.t2 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule symm :premises (t3.t2.t1))
% 7.54/7.82  (step t3.t2.t3 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) tptp.truth)) :rule symm :premises (t3.t2.a34))
% 7.54/7.82  (step t3.t2.t4 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) tptp.truth)) :rule symm :premises (t3.t2.a58))
% 7.54/7.82  (step t3.t2.t5 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule symm :premises (t3.t2.t4))
% 7.54/7.82  (step t3.t2.t6 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) :rule refl)
% 7.54/7.82  (step t3.t2.t7 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.truth)) :rule symm :premises (t3.t2.a57))
% 7.54/7.82  (step t3.t2.t8 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) tptp.truth)) :rule symm :premises (t3.t2.a15))
% 7.54/7.82  (step t3.t2.t9 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule symm :premises (t3.t2.t8))
% 7.54/7.82  (step t3.t2.t10 (cl (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b tptp.a))) :rule refl)
% 7.54/7.82  (step t3.t2.t11 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.a55))
% 7.54/7.82  (step t3.t2.t12 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule cong :premises (t3.t2.t10 t3.t2.t11))
% 7.54/7.82  (step t3.t2.t13 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule symm :premises (t3.t2.t12))
% 7.54/7.82  (step t3.t2.t14 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule trans :premises (t3.t2.t7 t3.t2.t9 t3.t2.t13))
% 7.54/7.82  (step t3.t2.t15 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule cong :premises (t3.t2.t6 t3.t2.t14))
% 7.54/7.82  (step t3.t2.t16 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule trans :premises (t3.t2.t5 t3.t2.t15))
% 7.54/7.82  (step t3.t2.t17 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule trans :premises (t3.t2.t3 t3.t2.t16))
% 7.54/7.82  (step t3.t2.t18 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule refl)
% 7.54/7.82  (step t3.t2.t19 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule cong :premises (t3.t2.t17 t3.t2.t18))
% 7.54/7.82  (step t3.t2.t20 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule symm :premises (t3.t2.a56))
% 7.54/7.82  (step t3.t2.t21 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.t20))
% 7.54/7.82  (step t3.t2.t22 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule refl)
% 7.54/7.82  (step t3.t2.t23 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) tptp.truth)) :rule trans :premises (t3.t2.t12 t3.t2.t8))
% 7.54/7.82  (step t3.t2.t24 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule cong :premises (t3.t2.t23 t3.t2.t6))
% 7.54/7.82  (step t3.t2.t25 (cl (= (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) :rule symm :premises (t3.t2.a54))
% 7.54/7.82  (step t3.t2.t26 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) :rule trans :premises (t3.t2.t24 t3.t2.t25))
% 7.54/7.82  (step t3.t2.t27 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.t26))
% 7.54/7.82  (step t3.t2.t28 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule cong :premises (t3.t2.t22 t3.t2.t27))
% 7.54/7.82  (step t3.t2.t29 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule cong :premises (t3.t2.t26 t3.t2.t26))
% 7.54/7.82  (step t3.t2.t30 (cl (= (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) :rule symm :premises (t3.t2.a53))
% 7.54/7.82  (step t3.t2.t31 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.t30))
% 7.54/7.82  (step t3.t2.t32 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.a52))
% 7.54/7.82  (step t3.t2.t33 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule symm :premises (t3.t2.t32))
% 7.54/7.82  (step t3.t2.t34 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) :rule refl)
% 7.54/7.82  (step t3.t2.t35 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) :rule refl)
% 7.54/7.82  (step t3.t2.t36 (cl (= (tptp.implies tptp.truth tptp.a) tptp.a)) :rule symm :premises (t3.t2.a51))
% 7.54/7.82  (step t3.t2.t37 (cl (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule symm :premises (t3.t2.t36))
% 7.54/7.82  (step t3.t2.t38 (cl (= tptp.a tptp.a)) :rule refl)
% 7.54/7.82  (step t3.t2.t39 (cl (= (tptp.implies tptp.truth tptp.a) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a))) :rule cong :premises (t3.t2.a12 t3.t2.t38))
% 7.54/7.82  (step t3.t2.t40 (cl (= tptp.a (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a))) :rule trans :premises (t3.t2.t37 t3.t2.t39))
% 7.54/7.82  (step t3.t2.t41 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)))) :rule cong :premises (t3.t2.t35 t3.t2.t40))
% 7.54/7.82  (step t3.t2.t42 (cl (= (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)))) :rule symm :premises (t3.t2.a50))
% 7.54/7.82  (step t3.t2.t43 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule symm :premises (t3.t2.t42))
% 7.54/7.82  (step t3.t2.t44 (cl (= (tptp.implies tptp.b tptp.b) tptp.truth)) :rule symm :premises (t3.t2.a12))
% 7.54/7.82  (step t3.t2.t45 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) tptp.truth)) :rule symm :premises (t3.t2.a49))
% 7.54/7.82  (step t3.t2.t46 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule symm :premises (t3.t2.t45))
% 7.54/7.82  (step t3.t2.t47 (cl (= (tptp.implies tptp.b tptp.b) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule trans :premises (t3.t2.t44 t3.t2.t46))
% 7.54/7.82  (step t3.t2.t48 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) :rule refl)
% 7.54/7.82  (step t3.t2.t49 (cl (= (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule cong :premises (t3.t2.t47 t3.t2.t48))
% 7.54/7.82  (step t3.t2.t50 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule symm :premises (t3.t2.a48))
% 7.54/7.82  (step t3.t2.t51 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule symm :premises (t3.t2.t50))
% 7.54/7.82  (step t3.t2.t52 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.a47))
% 7.54/7.82  (step t3.t2.t53 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule cong :premises (t3.t2.a46 t3.t2.t35))
% 7.54/7.82  (step t3.t2.t54 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.t53))
% 7.54/7.82  (step t3.t2.t55 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule trans :premises (t3.t2.t52 t3.t2.t54))
% 7.54/7.82  (step t3.t2.t56 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule symm :premises (t3.t2.a46))
% 7.54/7.82  (step t3.t2.t57 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.a0))
% 7.54/7.82  (step t3.t2.t58 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule trans :premises (t3.t2.t56 t3.t2.t57))
% 7.54/7.82  (step t3.t2.t59 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.t58))
% 7.54/7.82  (step t3.t2.t60 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule cong :premises (t3.t2.t59 t3.t2.t35))
% 7.54/7.82  (step t3.t2.t61 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.t60))
% 7.54/7.82  (step t3.t2.t62 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule trans :premises (t3.t2.t53 t3.t2.t61))
% 7.54/7.82  (step t3.t2.t63 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) :rule refl)
% 7.54/7.82  (step t3.t2.t64 (cl (= (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) tptp.truth)) :rule symm :premises (t3.t2.a3))
% 7.54/7.82  (step t3.t2.t65 (cl (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a tptp.b))) :rule refl)
% 7.54/7.82  (step t3.t2.t66 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule cong :premises (t3.t2.t64 t3.t2.t65))
% 7.54/7.82  (step t3.t2.t67 (cl (= (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule symm :premises (t3.t2.t66))
% 7.54/7.82  (step t3.t2.t68 (cl (= (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule trans :premises (t3.t2.a4 t3.t2.t67 t3.t2.a5))
% 7.54/7.82  (step t3.t2.t69 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))) :rule cong :premises (t3.t2.t63 t3.t2.t68))
% 7.54/7.82  (step t3.t2.t70 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))) :rule symm :premises (t3.t2.a45))
% 7.54/7.82  (step t3.t2.t71 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.t70))
% 7.54/7.82  (step t3.t2.t72 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule trans :premises (t3.t2.a0 t3.t2.t69 t3.t2.t71))
% 7.54/7.82  (step t3.t2.t73 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule trans :premises (t3.t2.t58 t3.t2.t72))
% 7.54/7.82  (step t3.t2.t74 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule cong :premises (t3.t2.t73 t3.t2.t35))
% 7.54/7.82  (step t3.t2.t75 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.a44))
% 7.54/7.82  (step t3.t2.t76 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule symm :premises (t3.t2.t75))
% 7.54/7.82  (step t3.t2.t77 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) :rule symm :premises (t3.t2.a18))
% 7.54/7.82  (step t3.t2.t78 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule symm :premises (t3.t2.t77))
% 7.54/7.82  (step t3.t2.t79 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule symm :premises (t3.t2.a17))
% 7.54/7.82  (step t3.t2.t80 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule symm :premises (t3.t2.t79))
% 7.54/7.82  (step t3.t2.t81 (cl (= (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) tptp.truth)) :rule symm :premises (t3.t2.a8))
% 7.54/7.82  (step t3.t2.t82 (cl (= (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule trans :premises (t3.t2.t81 t3.t2.a3))
% 7.54/7.82  (step t3.t2.t83 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule cong :premises (t3.t2.t65 t3.t2.t82))
% 7.54/7.82  (step t3.t2.t84 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) tptp.truth)) :rule symm :premises (t3.t2.a16))
% 7.54/7.82  (step t3.t2.t85 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) tptp.truth)) :rule trans :premises (t3.t2.t80 t3.t2.t83 t3.t2.t84))
% 7.54/7.82  (step t3.t2.t86 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule trans :premises (t3.t2.t85 t3.t2.t9))
% 7.54/7.82  (step t3.t2.t87 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule cong :premises (t3.t2.t86 t3.t2.t34))
% 7.54/7.82  (step t3.t2.t88 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.a14))
% 7.54/7.82  (step t3.t2.t89 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule trans :premises (t3.t2.t78 t3.t2.t87 t3.t2.t88))
% 7.54/7.82  (step t3.t2.t90 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule cong :premises (t3.t2.t8 t3.t2.t34))
% 7.54/7.82  (step t3.t2.t91 (cl (= (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.a22))
% 7.54/7.82  (step t3.t2.t92 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) :rule trans :premises (t3.t2.a14 t3.t2.t90 t3.t2.t91))
% 7.54/7.82  (step t3.t2.t93 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) :rule trans :premises (t3.t2.t89 t3.t2.t92))
% 7.54/7.82  (step t3.t2.t94 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) :rule cong :premises (t3.t2.a23 t3.t2.t38))
% 7.54/7.82  (step t3.t2.t95 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule cong :premises (t3.t2.t93 t3.t2.t94))
% 7.54/7.82  (step t3.t2.t96 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.a24))
% 7.54/7.82  (step t3.t2.t97 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule cong :premises (t3.t2.a23 t3.t2.t6))
% 7.54/7.82  (step t3.t2.t98 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.t97))
% 7.54/7.82  (step t3.t2.t99 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t95 t3.t2.t96 t3.t2.t98))
% 7.54/7.82  (step t3.t2.t100 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.a23))
% 7.54/7.82  (step t3.t2.t101 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.a9))
% 7.54/7.82  (step t3.t2.t102 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule cong :premises (t3.t2.t81 t3.t2.t10))
% 7.54/7.82  (step t3.t2.t103 (cl (= (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))) :rule symm :premises (t3.t2.a7))
% 7.54/7.82  (step t3.t2.t104 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) (tptp.implies tptp.b tptp.a))) :rule trans :premises (t3.t2.t101 t3.t2.t102 t3.t2.t103))
% 7.54/7.82  (step t3.t2.t105 (cl (= (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule symm :premises (t3.t2.t104))
% 7.54/7.82  (step t3.t2.t106 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule cong :premises (t3.t2.t34 t3.t2.t105))
% 7.54/7.82  (step t3.t2.t107 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.a21))
% 7.54/7.82  (step t3.t2.t108 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t106 t3.t2.t107))
% 7.54/7.82  (step t3.t2.t109 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t100 t3.t2.t108))
% 7.54/7.82  (step t3.t2.t110 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule cong :premises (t3.t2.t109 t3.t2.t6))
% 7.54/7.82  (step t3.t2.t111 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.a20))
% 7.54/7.82  (step t3.t2.t112 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule symm :premises (t3.t2.t111))
% 7.54/7.82  (step t3.t2.t113 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule symm :premises (t3.t2.a19))
% 7.54/7.82  (step t3.t2.t114 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule cong :premises (t3.t2.t10 t3.t2.t89))
% 7.54/7.82  (step t3.t2.t115 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))) tptp.truth)) :rule symm :premises (t3.t2.a13))
% 7.54/7.82  (step t3.t2.t116 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) tptp.truth)) :rule trans :premises (t3.t2.t113 t3.t2.t114 t3.t2.t115))
% 7.54/7.82  (step t3.t2.t117 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies tptp.b tptp.b))) :rule trans :premises (t3.t2.t116 t3.t2.a12))
% 7.54/7.82  (step t3.t2.t118 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) :rule refl)
% 7.54/7.82  (step t3.t2.t119 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule cong :premises (t3.t2.t117 t3.t2.t118))
% 7.54/7.82  (step t3.t2.t120 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) tptp.truth)) :rule symm :premises (t3.t2.a11))
% 7.54/7.82  (step t3.t2.t121 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule symm :premises (t3.t2.t120))
% 7.54/7.82  (step t3.t2.t122 (cl (= (tptp.implies tptp.b tptp.b) (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule trans :premises (t3.t2.t44 t3.t2.t121))
% 7.54/7.82  (step t3.t2.t123 (cl (= (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule cong :premises (t3.t2.t122 t3.t2.t118))
% 7.54/7.82  (step t3.t2.t124 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a))) :rule symm :premises (t3.t2.a10))
% 7.54/7.82  (step t3.t2.t125 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) :rule cong :premises (t3.t2.t104 t3.t2.t38))
% 7.54/7.82  (step t3.t2.t126 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) :rule trans :premises (t3.t2.t97 t3.t2.t110 t3.t2.t112 t3.t2.t119 t3.t2.t123 t3.t2.t124 t3.t2.t125))
% 7.54/7.82  (step t3.t2.t127 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) :rule symm :premises (t3.t2.a6))
% 7.54/7.82  (step t3.t2.t128 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule symm :premises (t3.t2.t127))
% 7.54/7.82  (step t3.t2.t129 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule trans :premises (t3.t2.t99 t3.t2.t126 t3.t2.t128))
% 7.54/7.82  (step t3.t2.t130 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.t129))
% 7.54/7.82  (step t3.t2.t131 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule cong :premises (t3.t2.t35 t3.t2.t130))
% 7.54/7.82  (step t3.t2.t132 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) :rule refl)
% 7.54/7.82  (step t3.t2.t133 (cl (= (tptp.implies tptp.truth tptp.b) tptp.b)) :rule symm :premises (t3.t2.a30))
% 7.54/7.82  (step t3.t2.t134 (cl (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule symm :premises (t3.t2.t133))
% 7.54/7.82  (step t3.t2.t135 (cl (= tptp.b tptp.b)) :rule refl)
% 7.54/7.82  (step t3.t2.t136 (cl (= (tptp.implies tptp.truth tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b))) :rule cong :premises (t3.t2.a28 t3.t2.t135))
% 7.54/7.82  (step t3.t2.t137 (cl (= tptp.b (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b))) :rule trans :premises (t3.t2.t134 t3.t2.t136))
% 7.54/7.82  (step t3.t2.t138 (cl (= (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b) tptp.b)) :rule symm :premises (t3.t2.t137))
% 7.54/7.82  (step t3.t2.t139 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule cong :premises (t3.t2.t132 t3.t2.t138))
% 7.54/7.82  (step t3.t2.t140 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)))) :rule symm :premises (t3.t2.t139))
% 7.54/7.82  (step t3.t2.t141 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies tptp.a tptp.a))) :rule trans :premises (t3.t2.t3 t3.t2.a28))
% 7.54/7.82  (step t3.t2.t142 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.a25))
% 7.54/7.82  (step t3.t2.t143 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t142 t3.t2.t98))
% 7.54/7.82  (step t3.t2.t144 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.t99))
% 7.54/7.82  (step t3.t2.t145 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t143 t3.t2.t144))
% 7.54/7.82  (step t3.t2.t146 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule symm :premises (t3.t2.t145))
% 7.54/7.82  (step t3.t2.t147 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule cong :premises (t3.t2.t141 t3.t2.t146))
% 7.54/7.82  (step t3.t2.t148 (cl (= (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule symm :premises (t3.t2.t147))
% 7.54/7.82  (step t3.t2.t149 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule trans :premises (t3.t2.t95 t3.t2.t96 t3.t2.a25 t3.t2.t140 t3.t2.a33 t3.t2.t148))
% 7.54/7.82  (step t3.t2.t150 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule cong :premises (t3.t2.t35 t3.t2.t149))
% 7.54/7.82  (step t3.t2.t151 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule symm :premises (t3.t2.a43))
% 7.54/7.82  (step t3.t2.t152 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule symm :premises (t3.t2.t151))
% 7.54/7.82  (step t3.t2.t153 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))) tptp.truth)) :rule symm :premises (t3.t2.a42))
% 7.54/7.82  (step t3.t2.t154 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule symm :premises (t3.t2.t153))
% 7.54/7.82  (step t3.t2.t155 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.t108))
% 7.54/7.82  (step t3.t2.t156 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule trans :premises (t3.t2.t155 t3.t2.a0))
% 7.54/7.82  (step t3.t2.t157 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule cong :premises (t3.t2.t128 t3.t2.t135))
% 7.54/7.82  (step t3.t2.t158 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule symm :premises (t3.t2.a5))
% 7.54/7.82  (step t3.t2.t159 (cl (= (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) :rule symm :premises (t3.t2.a4))
% 7.54/7.82  (step t3.t2.t160 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b) (tptp.implies tptp.a tptp.b))) :rule trans :premises (t3.t2.t157 t3.t2.t158 t3.t2.t66 t3.t2.t159))
% 7.54/7.82  (step t3.t2.t161 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule cong :premises (t3.t2.t156 t3.t2.t160))
% 7.54/7.82  (step t3.t2.t162 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule symm :premises (t3.t2.a41))
% 7.54/7.82  (step t3.t2.t163 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule symm :premises (t3.t2.t162))
% 7.54/7.82  (step t3.t2.t164 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) tptp.truth)) :rule symm :premises (t3.t2.a2))
% 7.54/7.82  (step t3.t2.t165 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule cong :premises (t3.t2.t164 t3.t2.t63))
% 7.54/7.82  (step t3.t2.t166 (cl (= (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) :rule symm :premises (t3.t2.a1))
% 7.54/7.82  (step t3.t2.t167 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) :rule trans :premises (t3.t2.t161 t3.t2.t163 t3.t2.t165 t3.t2.t166))
% 7.54/7.82  (step t3.t2.t168 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule cong :premises (t3.t2.t132 t3.t2.t167))
% 7.54/7.82  (step t3.t2.t169 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)))) :rule cong :premises (t3.t2.t6 t3.t2.t137))
% 7.54/7.82  (step t3.t2.t170 (cl (= (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)))) :rule symm :premises (t3.t2.a29))
% 7.54/7.82  (step t3.t2.t171 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule symm :premises (t3.t2.t170))
% 7.54/7.82  (step t3.t2.t172 (cl (= (tptp.implies tptp.a tptp.a) tptp.truth)) :rule symm :premises (t3.t2.a28))
% 7.54/7.82  (step t3.t2.t173 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) tptp.truth)) :rule symm :premises (t3.t2.a27))
% 7.54/7.82  (step t3.t2.t174 (cl (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule symm :premises (t3.t2.t173))
% 7.54/7.82  (step t3.t2.t175 (cl (= (tptp.implies tptp.a tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule trans :premises (t3.t2.t172 t3.t2.t174))
% 7.54/7.82  (step t3.t2.t176 (cl (= (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule cong :premises (t3.t2.t175 t3.t2.t132))
% 7.54/7.82  (step t3.t2.t177 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule symm :premises (t3.t2.a26))
% 7.54/7.82  (step t3.t2.t178 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule symm :premises (t3.t2.t177))
% 7.54/7.82  (step t3.t2.t179 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.b))) :rule cong :premises (t3.t2.t145 t3.t2.t135))
% 7.54/7.82  (step t3.t2.t180 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.t92))
% 7.54/7.82  (step t3.t2.t181 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule symm :premises (t3.t2.a40))
% 7.54/7.82  (step t3.t2.t182 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.t181))
% 7.54/7.82  (step t3.t2.t183 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule cong :premises (t3.t2.t135 t3.t2.t94))
% 7.54/7.82  (step t3.t2.t184 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t182 t3.t2.t183))
% 7.54/7.82  (step t3.t2.t185 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t180 t3.t2.t184))
% 7.54/7.82  (step t3.t2.t186 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) :rule refl)
% 7.54/7.82  (step t3.t2.t187 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule cong :premises (t3.t2.t185 t3.t2.t186))
% 7.54/7.82  (step t3.t2.t188 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule symm :premises (t3.t2.a39))
% 7.54/7.82  (step t3.t2.t189 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule symm :premises (t3.t2.t188))
% 7.54/7.82  (step t3.t2.t190 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule trans :premises (t3.t2.t95 t3.t2.t187 t3.t2.t189))
% 7.54/7.82  (step t3.t2.t191 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule cong :premises (t3.t2.t190 t3.t2.t135))
% 7.54/7.82  (step t3.t2.t192 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule symm :premises (t3.t2.a38))
% 7.54/7.82  (step t3.t2.t193 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule symm :premises (t3.t2.t192))
% 7.54/7.82  (step t3.t2.t194 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) :rule cong :premises (t3.t2.t94 t3.t2.t135))
% 7.54/7.82  (step t3.t2.t195 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) :rule symm :premises (t3.t2.t194))
% 7.54/7.82  (step t3.t2.t196 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule cong :premises (t3.t2.t135 t3.t2.t195))
% 7.54/7.82  (step t3.t2.t197 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) tptp.truth)) :rule symm :premises (t3.t2.a37))
% 7.54/7.82  (step t3.t2.t198 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) tptp.truth)) :rule trans :premises (t3.t2.t196 t3.t2.t197))
% 7.54/7.82  (step t3.t2.t199 (cl (= (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies tptp.a tptp.a))) :rule trans :premises (t3.t2.t198 t3.t2.a28))
% 7.54/7.82  (step t3.t2.t200 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule cong :premises (t3.t2.t199 t3.t2.t195))
% 7.54/7.82  (step t3.t2.t201 (cl (= (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)))) :rule symm :premises (t3.t2.a36))
% 7.54/7.82  (step t3.t2.t202 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) :rule refl)
% 7.54/7.82  (step t3.t2.t203 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) :rule cong :premises (t3.t2.t202 t3.t2.t138))
% 7.54/7.82  (step t3.t2.t204 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) :rule trans :premises (t3.t2.t169 t3.t2.t171 t3.t2.t176 t3.t2.t178 t3.t2.t179 t3.t2.t191 t3.t2.t193 t3.t2.t200 t3.t2.t201 t3.t2.t203 t3.t2.t194))
% 7.54/7.82  (step t3.t2.t205 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule cong :premises (t3.t2.t204 t3.t2.t63))
% 7.54/7.82  (step t3.t2.t206 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule trans :premises (t3.t2.t154 t3.t2.t168 t3.t2.t205))
% 7.54/7.82  (step t3.t2.t207 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule trans :premises (t3.t2.t3 t3.t2.t206))
% 7.54/7.82  (step t3.t2.t208 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule cong :premises (t3.t2.t35 t3.t2.t190))
% 7.54/7.82  (step t3.t2.t209 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule cong :premises (t3.t2.t207 t3.t2.t208))
% 7.54/7.82  (step t3.t2.t210 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) tptp.truth)) :rule symm :premises (t3.t2.a35))
% 7.54/7.82  (step t3.t2.t211 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) tptp.truth)) :rule trans :premises (t3.t2.t131 t3.t2.t150 t3.t2.t152 t3.t2.t209 t3.t2.t210))
% 7.54/7.82  (step t3.t2.t212 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule trans :premises (t3.t2.t211 t3.t2.a34))
% 7.54/7.82  (step t3.t2.t213 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule cong :premises (t3.t2.t212 t3.t2.t130))
% 7.54/7.82  (step t3.t2.t214 (cl (= (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)))) :rule symm :premises (t3.t2.a33))
% 7.54/7.82  (step t3.t2.t215 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule trans :premises (t3.t2.t60 t3.t2.t74 t3.t2.t76 t3.t2.t213 t3.t2.t147 t3.t2.t214 t3.t2.t139 t3.t2.t142 t3.t2.t98))
% 7.54/7.82  (step t3.t2.t216 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) :rule trans :premises (t3.t2.t55 t3.t2.t62 t3.t2.t215 t3.t2.t126))
% 7.54/7.82  (step t3.t2.t217 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule cong :premises (t3.t2.t216 t3.t2.t38))
% 7.54/7.82  (step t3.t2.t218 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) (tptp.implies tptp.b tptp.a))) :rule trans :premises (t3.t2.t41 t3.t2.t43 t3.t2.t49 t3.t2.t51 t3.t2.t217 t3.t2.t101 t3.t2.t102 t3.t2.t103))
% 7.54/7.82  (step t3.t2.t219 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule cong :premises (t3.t2.t34 t3.t2.t218))
% 7.54/7.82  (step t3.t2.t220 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule trans :premises (t3.t2.t33 t3.t2.t219))
% 7.54/7.82  (step t3.t2.t221 (cl (= (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule trans :premises (t3.t2.t64 t3.t2.a2))
% 7.54/7.82  (step t3.t2.t222 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule cong :premises (t3.t2.t221 t3.t2.t63))
% 7.54/7.82  (step t3.t2.t223 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule symm :premises (t3.t2.t222))
% 7.54/7.82  (step t3.t2.t224 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) :rule trans :premises (t3.t2.t222 t3.t2.t165 t3.t2.t166))
% 7.54/7.82  (step t3.t2.t225 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) :rule trans :premises (t3.t2.t223 t3.t2.t224))
% 7.54/7.82  (step t3.t2.t226 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule trans :premises (t3.t2.t164 t3.t2.t174))
% 7.54/7.82  (step t3.t2.t227 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule cong :premises (t3.t2.t226 t3.t2.t132))
% 7.54/7.82  (step t3.t2.t228 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule cong :premises (t3.t2.t129 t3.t2.t135))
% 7.54/7.82  (step t3.t2.t229 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies tptp.a tptp.b))) :rule trans :premises (t3.t2.t227 t3.t2.t178 t3.t2.t179 t3.t2.t228 t3.t2.t158 t3.t2.t66 t3.t2.t159))
% 7.54/7.82  (step t3.t2.t230 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule cong :premises (t3.t2.t225 t3.t2.t229))
% 7.54/7.82  (step t3.t2.t231 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule symm :premises (t3.t2.t230))
% 7.54/7.82  (step t3.t2.t232 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule symm :premises (t3.t2.t225))
% 7.54/7.82  (step t3.t2.t233 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule symm :premises (t3.t2.t227))
% 7.54/7.82  (step t3.t2.t234 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule trans :premises (t3.t2.t169 t3.t2.t171 t3.t2.t176 t3.t2.t233))
% 7.54/7.82  (step t3.t2.t235 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule cong :premises (t3.t2.t232 t3.t2.t234))
% 7.54/7.82  (step t3.t2.t236 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule symm :premises (t3.t2.t235))
% 7.54/7.82  (step t3.t2.t237 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule symm :premises (t3.t2.a31))
% 7.54/7.82  (step t3.t2.t238 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule trans :premises (t3.t2.a0 t3.t2.t231 t3.t2.t236 t3.t2.t237))
% 7.54/7.82  (step t3.t2.t239 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule trans :premises (t3.t2.t220 t3.t2.t238))
% 7.54/7.82  (step t3.t2.t240 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule refl)
% 7.54/7.82  (step t3.t2.t241 (cl (= (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule cong :premises (t3.t2.t239 t3.t2.t240 t3.t2.t6 t3.t2.t35))
% 7.54/7.82  (step t3.t2.t242 (cl (= (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) :rule symm :premises (t3.t2.a32))
% 7.54/7.82  (step t3.t2.t243 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) :rule trans :premises (t3.t2.t31 t3.t2.t241 t3.t2.t242))
% 7.54/7.82  (step t3.t2.t244 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule cong :premises (t3.t2.t6 t3.t2.t243))
% 7.54/7.82  (step t3.t2.t245 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule symm :premises (t3.t2.t237))
% 7.54/7.82  (step t3.t2.t246 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule trans :premises (t3.t2.t2 t3.t2.t19 t3.t2.t21 t3.t2.t28 t3.t2.t29 t3.t2.t244 t3.t2.t245 t3.t2.t235 t3.t2.t230 t3.t2.t57))
% 7.54/7.82  (step t3.t2 (cl (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (not (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.b tptp.b))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a tptp.a))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.b (tptp.implies tptp.truth tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= tptp.a (tptp.implies tptp.truth tptp.a))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3 t3.t2.a4 t3.t2.a5 t3.t2.a6 t3.t2.a7 t3.t2.a8 t3.t2.a9 t3.t2.a10 t3.t2.a11 t3.t2.a12 t3.t2.a13 t3.t2.a14 t3.t2.a15 t3.t2.a16 t3.t2.a17 t3.t2.a18 t3.t2.a19 t3.t2.a20 t3.t2.a21 t3.t2.a22 t3.t2.a23 t3.t2.a24 t3.t2.a25 t3.t2.a26 t3.t2.a27 t3.t2.a28 t3.t2.a29 t3.t2.a30 t3.t2.a31 t3.t2.a32 t3.t2.a33 t3.t2.a34 t3.t2.a35 t3.t2.a36 t3.t2.a37 t3.t2.a38 t3.t2.a39 t3.t2.a40 t3.t2.a41 t3.t2.a42 t3.t2.a43 t3.t2.a44 t3.t2.a45 t3.t2.a46 t3.t2.a47 t3.t2.a48 t3.t2.a49 t3.t2.a50 t3.t2.a51 t3.t2.a52 t3.t2.a53 t3.t2.a54 t3.t2.a55 t3.t2.a56 t3.t2.a57 t3.t2.a58 t3.t2.a59))
% 7.54/7.82  (step t3.t3 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule and_pos)
% 7.54/7.82  (step t3.t4 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.54/7.82  (step t3.t5 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.54/7.83  (step t3.t6 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t7 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t8 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.83  (step t3.t9 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.83  (step t3.t10 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t11 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t12 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule and_pos)
% 7.65/7.83  (step t3.t13 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t14 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t15 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule and_pos)
% 7.65/7.83  (step t3.t16 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.83  (step t3.t17 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.83  (step t3.t18 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.83  (step t3.t19 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.65/7.83  (step t3.t20 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.83  (step t3.t21 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.83  (step t3.t22 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t23 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t24 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t25 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.83  (step t3.t26 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t27 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t28 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.83  (step t3.t29 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.83  (step t3.t30 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t31 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule and_pos)
% 7.65/7.83  (step t3.t32 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t33 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule and_pos)
% 7.65/7.83  (step t3.t34 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t35 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t36 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t37 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t38 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule and_pos)
% 7.65/7.83  (step t3.t39 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t40 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t41 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t42 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.83  (step t3.t43 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t44 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.65/7.83  (step t3.t45 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule and_pos)
% 7.65/7.83  (step t3.t46 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule and_pos)
% 7.65/7.83  (step t3.t47 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t48 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t49 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t50 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule and_pos)
% 7.65/7.83  (step t3.t51 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule and_pos)
% 7.65/7.83  (step t3.t52 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t53 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t54 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule and_pos)
% 7.65/7.83  (step t3.t55 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t56 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.83  (step t3.t57 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t58 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t59 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t60 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.83  (step t3.t61 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule and_pos)
% 7.65/7.83  (step t3.t62 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule and_pos)
% 7.65/7.83  (step t3.t63 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6 t3.t7 t3.t8 t3.t9 t3.t10 t3.t11 t3.t12 t3.t13 t3.t14 t3.t15 t3.t16 t3.t17 t3.t18 t3.t19 t3.t20 t3.t21 t3.t22 t3.t23 t3.t24 t3.t25 t3.t26 t3.t27 t3.t28 t3.t29 t3.t30 t3.t31 t3.t32 t3.t33 t3.t34 t3.t35 t3.t36 t3.t37 t3.t38 t3.t39 t3.t40 t3.t41 t3.t42 t3.t43 t3.t44 t3.t45 t3.t46 t3.t47 t3.t48 t3.t49 t3.t50 t3.t51 t3.t52 t3.t53 t3.t54 t3.t55 t3.t56 t3.t57 t3.t58 t3.t59 t3.t60 t3.t61 t3.t62))
% 7.65/7.84  (step t3.t64 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule reordering :premises (t3.t63))
% 7.65/7.84  (step t3.t65 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule contraction :premises (t3.t64))
% 7.65/7.84  (step t3.t66 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t3.t1 t3.t65))
% 7.65/7.84  (step t3.t67 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule implies_neg2)
% 7.65/7.84  (step t3.t68 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t3.t66 t3.t67))
% 7.65/7.84  (step t3.t69 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule contraction :premises (t3.t68))
% 7.65/7.84  (step t3.t70 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule implies :premises (t3.t69))
% 7.65/7.84  (step t3.t71 (cl (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (not (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.b tptp.b))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a tptp.a))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.b (tptp.implies tptp.truth tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= tptp.a (tptp.implies tptp.truth tptp.a))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) :rule and_neg)
% 7.65/7.84  (step t3.t72 (cl (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) :rule resolution :premises (t3.t71 t3.a0 t3.a35 t3.a7 t3.a1 t3.a25 t3.a30 t3.a12 t3.a24 t3.a2 t3.a29 t3.a37 t3.a17 t3.a14 t3.a18 t3.a13 t3.a3 t3.a6 t3.a21 t3.a28 t3.a56 t3.a50 t3.a42 t3.a26 t3.a5 t3.a34 t3.a32 t3.a53 t3.a19 t3.a15 t3.a44 t3.a23 t3.a48 t3.a40 t3.a46 t3.a8 t3.a49 t3.a47 t3.a41 t3.a52 t3.a39 t3.a20 t3.a31 t3.a55 t3.a58 t3.a51 t3.a43 t3.a11 t3.a38 t3.a54 t3.a33 t3.a45 t3.a22 t3.a57 t3.a59 t3.a36 t3.a4 t3.a27 t3.a9 t3.a16 t3.a10))
% 7.65/7.84  (step t3.t73 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t3.t70 t3.t72))
% 7.65/7.84  (step t3 (cl (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b tptp.b))) (not (= tptp.truth (tptp.implies tptp.a tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (not (= tptp.a (tptp.implies tptp.truth tptp.a))) (not (= tptp.b (tptp.implies tptp.truth tptp.b))) (not (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (not (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3 t3.a4 t3.a5 t3.a6 t3.a7 t3.a8 t3.a9 t3.a10 t3.a11 t3.a12 t3.a13 t3.a14 t3.a15 t3.a16 t3.a17 t3.a18 t3.a19 t3.a20 t3.a21 t3.a22 t3.a23 t3.a24 t3.a25 t3.a26 t3.a27 t3.a28 t3.a29 t3.a30 t3.a31 t3.a32 t3.a33 t3.a34 t3.a35 t3.a36 t3.a37 t3.a38 t3.a39 t3.a40 t3.a41 t3.a42 t3.a43 t3.a44 t3.a45 t3.a46 t3.a47 t3.a48 t3.a49 t3.a50 t3.a51 t3.a52 t3.a53 t3.a54 t3.a55 t3.a56 t3.a57 t3.a58 t3.a59))
% 7.65/7.84  (step t4 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule and_pos)
% 7.65/7.84  (step t5 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule and_pos)
% 7.65/7.84  (step t6 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule and_pos)
% 7.65/7.84  (step t7 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.84  (step t8 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.84  (step t9 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.84  (step t10 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.65/7.84  (step t11 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.65/7.84  (step t12 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.84  (step t13 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.84  (step t14 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule and_pos)
% 7.65/7.84  (step t15 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.84  (step t16 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.84  (step t17 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.85  (step t18 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule and_pos)
% 7.65/7.85  (step t19 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule and_pos)
% 7.65/7.85  (step t20 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule and_pos)
% 7.65/7.85  (step t21 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t22 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.85  (step t23 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t24 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t25 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.85  (step t26 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule and_pos)
% 7.65/7.85  (step t27 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule and_pos)
% 7.65/7.85  (step t28 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t29 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t30 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.85  (step t31 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t32 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule and_pos)
% 7.65/7.85  (step t33 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule and_pos)
% 7.65/7.85  (step t34 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.85  (step t35 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.65/7.85  (step t36 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.85  (step t37 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t38 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t39 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule and_pos)
% 7.65/7.85  (step t40 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t41 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t42 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule and_pos)
% 7.65/7.85  (step t43 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.85  (step t44 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t45 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t46 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t47 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t48 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t49 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t50 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t51 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t52 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t53 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule and_pos)
% 7.65/7.85  (step t54 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t55 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t56 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t57 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule and_pos)
% 7.65/7.85  (step t58 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule and_pos)
% 7.65/7.85  (step t59 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule and_pos)
% 7.65/7.85  (step t60 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t61 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule and_pos)
% 7.65/7.85  (step t62 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule and_pos)
% 7.65/7.85  (step t63 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule and_pos)
% 7.65/7.85  (step t64 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t25 t26 t27 t28 t29 t30 t31 t32 t33 t34 t35 t36 t37 t38 t39 t40 t41 t42 t43 t44 t45 t46 t47 t48 t49 t50 t51 t52 t53 t54 t55 t56 t57 t58 t59 t60 t61 t62 t63))
% 7.65/7.86  (step t65 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule reordering :premises (t64))
% 7.65/7.86  (step t66 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule contraction :premises (t65))
% 7.65/7.86  (step t67 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t2 t66))
% 7.65/7.86  (step t68 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t69 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t67 t68))
% 7.65/7.86  (step t70 (cl (=> (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule contraction :premises (t69))
% 7.65/7.86  (step t71 (cl (not (and (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b tptp.b)) (= tptp.truth (tptp.implies tptp.a tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.a (tptp.implies tptp.truth tptp.a)) (= tptp.b (tptp.implies tptp.truth tptp.b)) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule implies :premises (t70))
% 7.65/7.86  (step t72 (cl (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b tptp.b))) (not (= tptp.truth (tptp.implies tptp.a tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (not (= tptp.a (tptp.implies tptp.truth tptp.a))) (not (= tptp.b (tptp.implies tptp.truth tptp.b))) (not (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (not (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t1 t71))
% 7.65/7.86  (step t73 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b tptp.b))) (not (= tptp.truth (tptp.implies tptp.a tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (not (= tptp.a (tptp.implies tptp.truth tptp.a))) (not (= tptp.b (tptp.implies tptp.truth tptp.b))) (not (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (not (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule reordering :premises (t72))
% 7.65/7.86  (step t74 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t75)
% 7.65/7.86  (assume t75.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))))
% 7.65/7.86  (step t75.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule forall_inst :args ((:= A (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (:= B (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= C (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.65/7.86  (step t75.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule or :premises (t75.t1))
% 7.65/7.86  (step t75.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t75.t2 t75.a0))
% 7.65/7.86  (step t75 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule subproof :discharge (t75.a0))
% 7.65/7.86  (step t76 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t74 t75))
% 7.65/7.86  (step t77 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t78 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule resolution :premises (t76 t77))
% 7.65/7.86  (step t79 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule contraction :premises (t78))
% 7.65/7.86  (step t80 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule implies :premises (t79))
% 7.65/7.86  (step t81 (cl (not (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.ifeq A A B C) B)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))))) (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.ifeq A A B C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C)))) :rule equiv_pos2)
% 7.65/7.86  (anchor :step t82 :args ((A $$unsorted) (:= A A) (B $$unsorted) (:= B B) (C $$unsorted) (:= C C)))
% 7.65/7.86  (step t82.t1 (cl (= A A)) :rule refl)
% 7.65/7.86  (step t82.t2 (cl (= B B)) :rule refl)
% 7.65/7.86  (step t82.t3 (cl (= C C)) :rule refl)
% 7.65/7.86  (step t82.t4 (cl (= (= (tptp.ifeq A A B C) B) (= B (tptp.ifeq A A B C)))) :rule all_simplify)
% 7.65/7.86  (step t82 (cl (= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.ifeq A A B C) B)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C))))) :rule bind)
% 7.65/7.86  (step t83 (cl (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= B (tptp.ifeq A A B C)))) :rule resolution :premises (t81 t82 a0))
% 7.65/7.86  (step t84 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t80 t83))
% 7.65/7.86  (step t85 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t86)
% 7.65/7.86  (assume t86.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t86.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (:= Y (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (:= Z (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))
% 7.65/7.86  (step t86.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule or :premises (t86.t1))
% 7.65/7.86  (step t86.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule resolution :premises (t86.t2 t86.a0))
% 7.65/7.86  (step t86 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule subproof :discharge (t86.a0))
% 7.65/7.86  (step t87 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule resolution :premises (t85 t86))
% 7.65/7.86  (step t88 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))))) :rule implies_neg2)
% 7.65/7.86  (step t89 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))))) :rule resolution :premises (t87 t88))
% 7.65/7.86  (step t90 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))))) :rule contraction :premises (t89))
% 7.65/7.86  (step t91 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule implies :premises (t90))
% 7.65/7.86  (step t92 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule resolution :premises (t91 a11))
% 7.65/7.86  (step t93 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t94)
% 7.65/7.86  (assume t94.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t94.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (:= Y (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (:= Z tptp.a)))
% 7.65/7.86  (step t94.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule or :premises (t94.t1))
% 7.65/7.86  (step t94.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t94.t2 t94.a0))
% 7.65/7.86  (step t94 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule subproof :discharge (t94.a0))
% 7.65/7.86  (step t95 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t93 t94))
% 7.65/7.86  (step t96 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t97 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule resolution :premises (t95 t96))
% 7.65/7.86  (step t98 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule contraction :premises (t97))
% 7.65/7.86  (step t99 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule implies :premises (t98))
% 7.65/7.86  (step t100 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t99 a11))
% 7.65/7.86  (step t101 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule equiv_pos2)
% 7.65/7.86  (step t102 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))) :rule refl)
% 7.65/7.86  (step t103 (cl (= (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule all_simplify)
% 7.65/7.86  (step t104 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))))) :rule cong :premises (t102 t103))
% 7.65/7.86  (step t105 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t106)
% 7.65/7.86  (assume t106.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t106.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y (tptp.implies tptp.b tptp.a)) (:= Z tptp.a)))
% 7.65/7.86  (step t106.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule or :premises (t106.t1))
% 7.65/7.86  (step t106.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule resolution :premises (t106.t2 t106.a0))
% 7.65/7.86  (step t106 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule subproof :discharge (t106.a0))
% 7.65/7.86  (step t107 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule resolution :premises (t105 t106))
% 7.65/7.86  (step t108 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))))) :rule resolution :premises (t107 t108))
% 7.65/7.86  (step t110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))))) :rule contraction :premises (t109))
% 7.65/7.86  (step t111 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule resolution :premises (t101 t104 t110))
% 7.65/7.86  (step t112 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule implies :premises (t111))
% 7.65/7.86  (step t113 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t112 a11))
% 7.65/7.86  (step t114 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t115)
% 7.65/7.86  (assume t115.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))))
% 7.65/7.86  (step t115.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y tptp.b) (:= Z (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))
% 7.65/7.86  (step t115.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule or :premises (t115.t1))
% 7.65/7.86  (step t115.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule resolution :premises (t115.t2 t115.a0))
% 7.65/7.86  (step t115 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule subproof :discharge (t115.a0))
% 7.65/7.86  (step t116 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule resolution :premises (t114 t115))
% 7.65/7.86  (step t117 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))))) :rule implies_neg2)
% 7.65/7.86  (step t118 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))))) :rule resolution :premises (t116 t117))
% 7.65/7.86  (step t119 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b)))))) :rule contraction :premises (t118))
% 7.65/7.86  (step t120 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule implies :premises (t119))
% 7.65/7.86  (step t121 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))))) (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) :rule equiv_pos2)
% 7.65/7.86  (anchor :step t122 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (Z $$unsorted) (:= Z Z)))
% 7.65/7.86  (step t122.t1 (cl (= X X)) :rule refl)
% 7.65/7.86  (step t122.t2 (cl (= Y Y)) :rule refl)
% 7.65/7.86  (step t122.t3 (cl (= Z Z)) :rule refl)
% 7.65/7.86  (step t122.t4 (cl (= (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))) tptp.truth) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) :rule all_simplify)
% 7.65/7.86  (step t122 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))))) :rule bind)
% 7.65/7.86  (step t123 (cl (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) :rule resolution :premises (t121 t122 a10))
% 7.65/7.86  (step t124 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.b))))) :rule resolution :premises (t120 t123))
% 7.65/7.86  (step t125 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t126)
% 7.65/7.86  (assume t126.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t126.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))
% 7.65/7.86  (step t126.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule or :premises (t126.t1))
% 7.65/7.86  (step t126.t3 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t126.t2 t126.a0))
% 7.65/7.86  (step t126 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule subproof :discharge (t126.a0))
% 7.65/7.86  (step t127 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t125 t126))
% 7.65/7.86  (step t128 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)))) :rule implies_neg2)
% 7.65/7.86  (step t129 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)))) :rule resolution :premises (t127 t128))
% 7.65/7.86  (step t130 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a)))) :rule contraction :premises (t129))
% 7.65/7.86  (step t131 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule implies :premises (t130))
% 7.65/7.86  (step t132 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t131 a3))
% 7.65/7.86  (step t133 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t134)
% 7.65/7.86  (assume t134.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t134.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))
% 7.65/7.86  (step t134.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule or :premises (t134.t1))
% 7.65/7.86  (step t134.t3 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule resolution :premises (t134.t2 t134.a0))
% 7.65/7.86  (step t134 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule subproof :discharge (t134.a0))
% 7.65/7.86  (step t135 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule resolution :premises (t133 t134))
% 7.65/7.86  (step t136 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)))) :rule implies_neg2)
% 7.65/7.86  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)))) :rule resolution :premises (t135 t136))
% 7.65/7.86  (step t138 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b)))) :rule contraction :premises (t137))
% 7.65/7.86  (step t139 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule implies :premises (t138))
% 7.65/7.86  (step t140 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b))) :rule resolution :premises (t139 a3))
% 7.65/7.86  (step t141 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t142)
% 7.65/7.86  (assume t142.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t142.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (:= Y tptp.b)))
% 7.65/7.86  (step t142.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule or :premises (t142.t1))
% 7.65/7.86  (step t142.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t142.t2 t142.a0))
% 7.65/7.86  (step t142 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule subproof :discharge (t142.a0))
% 7.65/7.86  (step t143 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t141 t142))
% 7.65/7.86  (step t144 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t145 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))))) :rule resolution :premises (t143 t144))
% 7.65/7.86  (step t146 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b))))) :rule contraction :premises (t145))
% 7.65/7.86  (step t147 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule implies :premises (t146))
% 7.65/7.86  (step t148 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b) tptp.b) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t147 a3))
% 7.65/7.86  (step t149 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t150)
% 7.65/7.86  (assume t150.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t150.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.65/7.86  (step t150.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule or :premises (t150.t1))
% 7.65/7.86  (step t150.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule resolution :premises (t150.t2 t150.a0))
% 7.65/7.86  (step t150 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule subproof :discharge (t150.a0))
% 7.65/7.86  (step t151 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule resolution :premises (t149 t150))
% 7.65/7.86  (step t152 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t153 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))))) :rule resolution :premises (t151 t152))
% 7.65/7.86  (step t154 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))))) :rule contraction :premises (t153))
% 7.65/7.86  (step t155 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule implies :premises (t154))
% 7.65/7.86  (step t156 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule resolution :premises (t155 a3))
% 7.65/7.86  (step t157 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t158)
% 7.65/7.86  (assume t158.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t158.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.65/7.86  (step t158.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule or :premises (t158.t1))
% 7.65/7.86  (step t158.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t158.t2 t158.a0))
% 7.65/7.86  (step t158 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule subproof :discharge (t158.a0))
% 7.65/7.86  (step t159 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t157 t158))
% 7.65/7.86  (step t160 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t161 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule resolution :premises (t159 t160))
% 7.65/7.86  (step t162 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule contraction :premises (t161))
% 7.65/7.86  (step t163 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule implies :premises (t162))
% 7.65/7.86  (step t164 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t163 a3))
% 7.65/7.86  (step t165 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t166)
% 7.65/7.86  (assume t166.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))))
% 7.65/7.86  (step t166.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b)) (:= Y (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (:= Z tptp.b)))
% 7.65/7.86  (step t166.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule or :premises (t166.t1))
% 7.65/7.86  (step t166.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule resolution :premises (t166.t2 t166.a0))
% 7.65/7.86  (step t166 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule subproof :discharge (t166.a0))
% 7.65/7.86  (step t167 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule resolution :premises (t165 t166))
% 7.65/7.86  (step t168 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))))) :rule implies_neg2)
% 7.65/7.86  (step t169 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))))) :rule resolution :premises (t167 t168))
% 7.65/7.86  (step t170 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))))) :rule contraction :premises (t169))
% 7.65/7.86  (step t171 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule implies :premises (t170))
% 7.65/7.86  (step t172 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))))) (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule equiv_pos2)
% 7.65/7.86  (anchor :step t173 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y) (Z $$unsorted) (:= Z Z)))
% 7.65/7.86  (step t173.t1 (cl (= X X)) :rule refl)
% 7.65/7.86  (step t173.t2 (cl (= Y Y)) :rule refl)
% 7.65/7.86  (step t173.t3 (cl (= Z Z)) :rule refl)
% 7.65/7.86  (step t173.t4 (cl (= (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule all_simplify)
% 7.65/7.86  (step t173 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z))))))) :rule bind)
% 7.65/7.86  (step t174 (cl (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Y Z) (tptp.implies X Z)))))) :rule resolution :premises (t172 t173 a2))
% 7.65/7.86  (step t175 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule resolution :premises (t171 t174))
% 7.65/7.86  (step t176 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t177)
% 7.65/7.86  (assume t177.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t177.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (:= Z tptp.b)))
% 7.65/7.86  (step t177.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule or :premises (t177.t1))
% 7.65/7.86  (step t177.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t177.t2 t177.a0))
% 7.65/7.86  (step t177 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule subproof :discharge (t177.a0))
% 7.65/7.86  (step t178 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t176 t177))
% 7.65/7.86  (step t179 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t180 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule resolution :premises (t178 t179))
% 7.65/7.86  (step t181 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule contraction :premises (t180))
% 7.65/7.86  (step t182 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule implies :premises (t181))
% 7.65/7.86  (step t183 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t182 a11))
% 7.65/7.86  (step t184 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t185)
% 7.65/7.86  (assume t185.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t185.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y (tptp.implies tptp.a tptp.a)) (:= Z tptp.b)))
% 7.65/7.86  (step t185.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule or :premises (t185.t1))
% 7.65/7.86  (step t185.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t185.t2 t185.a0))
% 7.65/7.86  (step t185 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule subproof :discharge (t185.a0))
% 7.65/7.86  (step t186 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t184 t185))
% 7.65/7.86  (step t187 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t188 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule resolution :premises (t186 t187))
% 7.65/7.86  (step t189 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule contraction :premises (t188))
% 7.65/7.86  (step t190 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule implies :premises (t189))
% 7.65/7.86  (step t191 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t190 a11))
% 7.65/7.86  (step t192 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t193)
% 7.65/7.86  (assume t193.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t193.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)) (:= Y (tptp.implies tptp.a tptp.a)) (:= Z tptp.b)))
% 7.65/7.86  (step t193.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule or :premises (t193.t1))
% 7.65/7.86  (step t193.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule resolution :premises (t193.t2 t193.a0))
% 7.65/7.86  (step t193 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule subproof :discharge (t193.a0))
% 7.65/7.86  (step t194 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule resolution :premises (t192 t193))
% 7.65/7.86  (step t195 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t196 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule resolution :premises (t194 t195))
% 7.65/7.86  (step t197 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))))) :rule contraction :premises (t196))
% 7.65/7.86  (step t198 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule implies :premises (t197))
% 7.65/7.86  (step t199 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule resolution :premises (t198 a11))
% 7.65/7.86  (step t200 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t201)
% 7.65/7.86  (assume t201.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t201.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (:= Y (tptp.implies tptp.b tptp.b)) (:= Z tptp.a)))
% 7.65/7.86  (step t201.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule or :premises (t201.t1))
% 7.65/7.86  (step t201.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t201.t2 t201.a0))
% 7.65/7.86  (step t201 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule subproof :discharge (t201.a0))
% 7.65/7.86  (step t202 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t200 t201))
% 7.65/7.86  (step t203 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t204 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule resolution :premises (t202 t203))
% 7.65/7.86  (step t205 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule contraction :premises (t204))
% 7.65/7.86  (step t206 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule implies :premises (t205))
% 7.65/7.86  (step t207 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies tptp.b tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.b) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t206 a11))
% 7.65/7.86  (step t208 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t209)
% 7.65/7.86  (assume t209.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t209.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y (tptp.implies tptp.a tptp.a)) (:= Z tptp.b)))
% 7.65/7.86  (step t209.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule or :premises (t209.t1))
% 7.65/7.86  (step t209.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t209.t2 t209.a0))
% 7.65/7.86  (step t209 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule subproof :discharge (t209.a0))
% 7.65/7.86  (step t210 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t208 t209))
% 7.65/7.86  (step t211 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t212 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule resolution :premises (t210 t211))
% 7.65/7.86  (step t213 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule contraction :premises (t212))
% 7.65/7.86  (step t214 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule implies :premises (t213))
% 7.65/7.86  (step t215 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.a) tptp.b)) (tptp.implies (tptp.implies tptp.a tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t214 a11))
% 7.65/7.86  (step t216 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t217)
% 7.65/7.86  (assume t217.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t217.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (:= Y (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)) (:= Z tptp.b)))
% 7.65/7.86  (step t217.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule or :premises (t217.t1))
% 7.65/7.86  (step t217.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t217.t2 t217.a0))
% 7.65/7.86  (step t217 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule subproof :discharge (t217.a0))
% 7.65/7.86  (step t218 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t216 t217))
% 7.65/7.86  (step t219 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t220 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule resolution :premises (t218 t219))
% 7.65/7.86  (step t221 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule contraction :premises (t220))
% 7.65/7.86  (step t222 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule implies :premises (t221))
% 7.65/7.86  (step t223 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t222 a11))
% 7.65/7.86  (step t224 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))))) :rule equiv_pos2)
% 7.65/7.86  (step t225 (cl (= (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))))) :rule all_simplify)
% 7.65/7.86  (step t226 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))))) :rule cong :premises (t102 t225))
% 7.65/7.86  (step t227 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t228)
% 7.65/7.86  (assume t228.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t228.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (:= Y (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (:= Z tptp.a)))
% 7.65/7.86  (step t228.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule or :premises (t228.t1))
% 7.65/7.86  (step t228.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t228.t2 t228.a0))
% 7.65/7.86  (step t228 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule subproof :discharge (t228.a0))
% 7.65/7.86  (step t229 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t227 t228))
% 7.65/7.86  (step t230 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t231 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t229 t230))
% 7.65/7.86  (step t232 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule contraction :premises (t231))
% 7.65/7.86  (step t233 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))))) :rule resolution :premises (t224 t226 t232))
% 7.65/7.86  (step t234 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule implies :premises (t233))
% 7.65/7.86  (step t235 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule resolution :premises (t234 a11))
% 7.65/7.86  (step t236 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t237)
% 7.65/7.86  (assume t237.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.86  (step t237.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.65/7.86  (step t237.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule or :premises (t237.t1))
% 7.65/7.86  (step t237.t3 (cl (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t237.t2 t237.a0))
% 7.65/7.86  (step t237 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule subproof :discharge (t237.a0))
% 7.65/7.86  (step t238 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t236 t237))
% 7.65/7.86  (step t239 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t240 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule resolution :premises (t238 t239))
% 7.65/7.86  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule contraction :premises (t240))
% 7.65/7.86  (step t242 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule implies :premises (t241))
% 7.65/7.86  (step t243 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X (tptp.implies Y X)) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X (tptp.implies Y X)) tptp.truth))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule equiv_pos2)
% 7.65/7.86  (anchor :step t244 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 7.65/7.86  (step t244.t1 (cl (= X X)) :rule refl)
% 7.65/7.86  (step t244.t2 (cl (= Y Y)) :rule refl)
% 7.65/7.86  (step t244.t3 (cl (= (= (tptp.implies X (tptp.implies Y X)) tptp.truth) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule all_simplify)
% 7.65/7.86  (step t244 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies X (tptp.implies Y X)) tptp.truth)) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))) :rule bind)
% 7.65/7.86  (step t245 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule resolution :premises (t243 t244 a8))
% 7.65/7.86  (step t246 (cl (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t242 t245))
% 7.65/7.86  (step t247 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t248)
% 7.65/7.86  (assume t248.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))))
% 7.65/7.86  (step t248.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.65/7.86  (step t248.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule or :premises (t248.t1))
% 7.65/7.86  (step t248.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t248.t2 t248.a0))
% 7.65/7.86  (step t248 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule subproof :discharge (t248.a0))
% 7.65/7.86  (step t249 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t247 t248))
% 7.65/7.86  (step t250 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule implies_neg2)
% 7.65/7.86  (step t251 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule resolution :premises (t249 t250))
% 7.65/7.86  (step t252 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule contraction :premises (t251))
% 7.65/7.86  (step t253 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule implies :premises (t252))
% 7.65/7.86  (step t254 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) :rule equiv_pos2)
% 7.65/7.86  (anchor :step t255 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 7.65/7.86  (step t255.t1 (cl (= X X)) :rule refl)
% 7.65/7.86  (step t255.t2 (cl (= Y Y)) :rule refl)
% 7.65/7.86  (step t255.t3 (cl (= (= (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y) Y) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) :rule all_simplify)
% 7.65/7.86  (step t255 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y))))) :rule bind)
% 7.65/7.86  (step t256 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.ifeq (tptp.implies X Y) (tptp.implies Y X) X Y)))) :rule resolution :premises (t254 t255 a6))
% 7.65/7.86  (step t257 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.ifeq (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t253 t256))
% 7.65/7.86  (step t258 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t259)
% 7.65/7.86  (assume t259.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t259.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))))
% 7.65/7.86  (step t259.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule or :premises (t259.t1))
% 7.65/7.86  (step t259.t3 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule resolution :premises (t259.t2 t259.a0))
% 7.65/7.86  (step t259 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule subproof :discharge (t259.a0))
% 7.65/7.86  (step t260 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule resolution :premises (t258 t259))
% 7.65/7.86  (step t261 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule implies_neg2)
% 7.65/7.86  (step t262 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule resolution :premises (t260 t261))
% 7.65/7.86  (step t263 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule contraction :premises (t262))
% 7.65/7.86  (step t264 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule implies :premises (t263))
% 7.65/7.86  (step t265 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a) tptp.b) tptp.b))) :rule resolution :premises (t264 a3))
% 7.65/7.86  (step t266 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t267)
% 7.65/7.86  (assume t267.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t267.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.65/7.86  (step t267.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule or :premises (t267.t1))
% 7.65/7.86  (step t267.t3 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule resolution :premises (t267.t2 t267.a0))
% 7.65/7.86  (step t267 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule subproof :discharge (t267.a0))
% 7.65/7.86  (step t268 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule resolution :premises (t266 t267))
% 7.65/7.86  (step t269 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)))) :rule implies_neg2)
% 7.65/7.86  (step t270 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)))) :rule resolution :premises (t268 t269))
% 7.65/7.86  (step t271 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a)))) :rule contraction :premises (t270))
% 7.65/7.86  (step t272 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule implies :premises (t271))
% 7.65/7.86  (step t273 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a) tptp.a))) :rule resolution :premises (t272 a3))
% 7.65/7.86  (step t274 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t275)
% 7.65/7.86  (assume t275.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t275.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (:= Y tptp.a)))
% 7.65/7.86  (step t275.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule or :premises (t275.t1))
% 7.65/7.86  (step t275.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t275.t2 t275.a0))
% 7.65/7.86  (step t275 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule subproof :discharge (t275.a0))
% 7.65/7.86  (step t276 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t274 t275))
% 7.65/7.86  (step t277 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t278 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule resolution :premises (t276 t277))
% 7.65/7.86  (step t279 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule contraction :premises (t278))
% 7.65/7.86  (step t280 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule implies :premises (t279))
% 7.65/7.86  (step t281 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t280 a3))
% 7.65/7.86  (step t282 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t283)
% 7.65/7.86  (assume t283.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 7.65/7.86  (step t283.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.65/7.86  (step t283.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule or :premises (t283.t1))
% 7.65/7.86  (step t283.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t283.t2 t283.a0))
% 7.65/7.86  (step t283 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule subproof :discharge (t283.a0))
% 7.65/7.86  (step t284 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t282 t283))
% 7.65/7.86  (step t285 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t286 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t284 t285))
% 7.65/7.86  (step t287 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule contraction :premises (t286))
% 7.65/7.86  (step t288 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule implies :premises (t287))
% 7.65/7.86  (step t289 (cl (not (= (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X)) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))) (not (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule equiv_pos2)
% 7.65/7.86  (anchor :step t290 :args ((X $$unsorted) (:= X X)))
% 7.65/7.86  (step t290.t1 (cl (= X X)) :rule refl)
% 7.65/7.86  (step t290.t2 (cl (= (= (tptp.implies tptp.truth X) X) (= X (tptp.implies tptp.truth X)))) :rule all_simplify)
% 7.65/7.86  (step t290 (cl (= (forall ((X $$unsorted)) (= (tptp.implies tptp.truth X) X)) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))) :rule bind)
% 7.65/7.86  (step t291 (cl (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule resolution :premises (t289 t290 a1))
% 7.65/7.86  (step t292 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t288 t291))
% 7.65/7.86  (step t293 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t294)
% 7.65/7.86  (assume t294.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 7.65/7.86  (step t294.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))
% 7.65/7.86  (step t294.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule or :premises (t294.t1))
% 7.65/7.86  (step t294.t3 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t294.t2 t294.a0))
% 7.65/7.86  (step t294 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule subproof :discharge (t294.a0))
% 7.65/7.86  (step t295 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t293 t294))
% 7.65/7.86  (step t296 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule implies_neg2)
% 7.65/7.86  (step t297 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule resolution :premises (t295 t296))
% 7.65/7.86  (step t298 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule contraction :premises (t297))
% 7.65/7.86  (step t299 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule implies :premises (t298))
% 7.65/7.86  (step t300 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t299 t291))
% 7.65/7.86  (step t301 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t302)
% 7.65/7.86  (assume t302.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.86  (step t302.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))) (:= Y (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (:= Z tptp.a)))
% 7.65/7.86  (step t302.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule or :premises (t302.t1))
% 7.65/7.86  (step t302.t3 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule resolution :premises (t302.t2 t302.a0))
% 7.65/7.86  (step t302 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule subproof :discharge (t302.a0))
% 7.65/7.86  (step t303 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule resolution :premises (t301 t302))
% 7.65/7.86  (step t304 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t305 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))))) :rule resolution :premises (t303 t304))
% 7.65/7.86  (step t306 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a))))) :rule contraction :premises (t305))
% 7.65/7.86  (step t307 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule implies :premises (t306))
% 7.65/7.86  (step t308 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) tptp.a)))) :rule resolution :premises (t307 a11))
% 7.65/7.86  (step t309 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t310)
% 7.65/7.86  (assume t310.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.86  (step t310.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))
% 7.65/7.86  (step t310.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule or :premises (t310.t1))
% 7.65/7.86  (step t310.t3 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t310.t2 t310.a0))
% 7.65/7.86  (step t310 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule subproof :discharge (t310.a0))
% 7.65/7.86  (step t311 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t309 t310))
% 7.65/7.86  (step t312 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule implies_neg2)
% 7.65/7.86  (step t313 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule resolution :premises (t311 t312))
% 7.65/7.86  (step t314 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a))))) :rule contraction :premises (t313))
% 7.65/7.86  (step t315 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule implies :premises (t314))
% 7.65/7.86  (step t316 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b) tptp.a)))) :rule resolution :premises (t315 t245))
% 7.65/7.86  (step t317 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t318)
% 7.65/7.86  (assume t318.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t318.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.65/7.86  (step t318.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule or :premises (t318.t1))
% 7.65/7.86  (step t318.t3 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule resolution :premises (t318.t2 t318.a0))
% 7.65/7.86  (step t318 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule subproof :discharge (t318.a0))
% 7.65/7.86  (step t319 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule resolution :premises (t317 t318))
% 7.65/7.86  (step t320 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule implies_neg2)
% 7.65/7.86  (step t321 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule resolution :premises (t319 t320))
% 7.65/7.86  (step t322 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b)))) :rule contraction :premises (t321))
% 7.65/7.86  (step t323 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule implies :premises (t322))
% 7.65/7.86  (step t324 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b) tptp.b))) :rule resolution :premises (t323 a3))
% 7.65/7.86  (step t325 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.86  (anchor :step t326)
% 7.65/7.86  (assume t326.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.86  (step t326.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (:= Y (tptp.implies tptp.a tptp.b))))
% 7.65/7.86  (step t326.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule or :premises (t326.t1))
% 7.65/7.86  (step t326.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t326.t2 t326.a0))
% 7.65/7.86  (step t326 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule subproof :discharge (t326.a0))
% 7.65/7.86  (step t327 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t325 t326))
% 7.65/7.86  (step t328 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule implies_neg2)
% 7.65/7.86  (step t329 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule resolution :premises (t327 t328))
% 7.65/7.87  (step t330 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule contraction :premises (t329))
% 7.65/7.87  (step t331 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule implies :premises (t330))
% 7.65/7.87  (step t332 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t331 a3))
% 7.65/7.87  (step t333 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t334)
% 7.65/7.87  (assume t334.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.87  (step t334.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.implies tptp.a tptp.b))))
% 7.65/7.87  (step t334.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule or :premises (t334.t1))
% 7.65/7.87  (step t334.t3 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule resolution :premises (t334.t2 t334.a0))
% 7.65/7.87  (step t334 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule subproof :discharge (t334.a0))
% 7.65/7.87  (step t335 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule resolution :premises (t333 t334))
% 7.65/7.87  (step t336 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))) :rule implies_neg2)
% 7.65/7.87  (step t337 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))) :rule resolution :premises (t335 t336))
% 7.65/7.87  (step t338 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b)))) :rule contraction :premises (t337))
% 7.65/7.87  (step t339 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule implies :premises (t338))
% 7.65/7.87  (step t340 (cl (= (tptp.implies (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b) tptp.b))) :rule resolution :premises (t339 a3))
% 7.65/7.87  (step t341 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t342)
% 7.65/7.87  (assume t342.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.87  (step t342.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies tptp.b tptp.a))))
% 7.65/7.87  (step t342.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule or :premises (t342.t1))
% 7.65/7.87  (step t342.t3 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t342.t2 t342.a0))
% 7.65/7.87  (step t342 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule subproof :discharge (t342.a0))
% 7.65/7.87  (step t343 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t341 t342))
% 7.65/7.87  (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule implies_neg2)
% 7.65/7.87  (step t345 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule resolution :premises (t343 t344))
% 7.65/7.87  (step t346 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a)))) :rule contraction :premises (t345))
% 7.65/7.87  (step t347 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule implies :premises (t346))
% 7.65/7.87  (step t348 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) tptp.a))) :rule resolution :premises (t347 a3))
% 7.65/7.87  (step t349 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule equiv_pos2)
% 7.65/7.87  (step t350 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))) :rule refl)
% 7.65/7.87  (step t351 (cl (= (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule all_simplify)
% 7.65/7.87  (step t352 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))))) :rule cong :premises (t350 t351))
% 7.65/7.87  (step t353 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t354)
% 7.65/7.87  (assume t354.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.87  (step t354.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.65/7.87  (step t354.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) :rule or :premises (t354.t1))
% 7.65/7.87  (step t354.t3 (cl (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) :rule resolution :premises (t354.t2 t354.a0))
% 7.65/7.87  (step t354 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) :rule subproof :discharge (t354.a0))
% 7.65/7.87  (step t355 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) :rule resolution :premises (t353 t354))
% 7.65/7.87  (step t356 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) (not (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule implies_neg2)
% 7.65/7.87  (step t357 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule resolution :premises (t355 t356))
% 7.65/7.87  (step t358 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a)))) :rule contraction :premises (t357))
% 7.65/7.87  (step t359 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule resolution :premises (t349 t352 t358))
% 7.65/7.87  (step t360 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule implies :premises (t359))
% 7.65/7.87  (step t361 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t360 a3))
% 7.65/7.87  (step t362 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t363)
% 7.65/7.87  (assume t363.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.87  (step t363.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))
% 7.65/7.87  (step t363.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule or :premises (t363.t1))
% 7.65/7.87  (step t363.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t363.t2 t363.a0))
% 7.65/7.87  (step t363 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule subproof :discharge (t363.a0))
% 7.65/7.87  (step t364 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t362 t363))
% 7.65/7.87  (step t365 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t366 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t364 t365))
% 7.65/7.87  (step t367 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule contraction :premises (t366))
% 7.65/7.87  (step t368 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule implies :premises (t367))
% 7.65/7.87  (step t369 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t368 a3))
% 7.65/7.87  (step t370 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t371)
% 7.65/7.87  (assume t371.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 7.65/7.87  (step t371.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.65/7.87  (step t371.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule or :premises (t371.t1))
% 7.65/7.87  (step t371.t3 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t371.t2 t371.a0))
% 7.65/7.87  (step t371 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule subproof :discharge (t371.a0))
% 7.65/7.87  (step t372 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t370 t371))
% 7.65/7.87  (step t373 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule implies_neg2)
% 7.65/7.87  (step t374 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule resolution :premises (t372 t373))
% 7.65/7.87  (step t375 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule contraction :premises (t374))
% 7.65/7.87  (step t376 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule implies :premises (t375))
% 7.65/7.87  (step t377 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t376 t291))
% 7.65/7.87  (step t378 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t379)
% 7.65/7.87  (assume t379.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 7.65/7.87  (step t379.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies tptp.a tptp.b))))
% 7.65/7.87  (step t379.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule or :premises (t379.t1))
% 7.65/7.87  (step t379.t3 (cl (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t379.t2 t379.a0))
% 7.65/7.87  (step t379 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule subproof :discharge (t379.a0))
% 7.65/7.87  (step t380 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t378 t379))
% 7.65/7.87  (step t381 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))))) :rule implies_neg2)
% 7.65/7.87  (step t382 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t380 t381))
% 7.65/7.87  (step t383 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b))))) :rule contraction :premises (t382))
% 7.65/7.87  (step t384 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule implies :premises (t383))
% 7.65/7.87  (step t385 (cl (= (tptp.implies tptp.a tptp.b) (tptp.implies tptp.truth (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t384 t291))
% 7.65/7.87  (step t386 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t387)
% 7.65/7.87  (assume t387.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 7.65/7.87  (step t387.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies tptp.b tptp.a))))
% 7.65/7.87  (step t387.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule or :premises (t387.t1))
% 7.65/7.87  (step t387.t3 (cl (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t387.t2 t387.a0))
% 7.65/7.87  (step t387 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule subproof :discharge (t387.a0))
% 7.65/7.87  (step t388 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t386 t387))
% 7.65/7.87  (step t389 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (not (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t390 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t388 t389))
% 7.65/7.87  (step t391 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a))))) :rule contraction :premises (t390))
% 7.65/7.87  (step t392 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule implies :premises (t391))
% 7.65/7.87  (step t393 (cl (= (tptp.implies tptp.b tptp.a) (tptp.implies tptp.truth (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t392 t291))
% 7.65/7.87  (step t394 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.b (tptp.implies tptp.truth tptp.b))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t395)
% 7.65/7.87  (assume t395.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 7.65/7.87  (step t395.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.b (tptp.implies tptp.truth tptp.b)))) :rule forall_inst :args ((:= X tptp.b)))
% 7.65/7.87  (step t395.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule or :premises (t395.t1))
% 7.65/7.87  (step t395.t3 (cl (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule resolution :premises (t395.t2 t395.a0))
% 7.65/7.87  (step t395 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule subproof :discharge (t395.a0))
% 7.65/7.87  (step t396 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.b (tptp.implies tptp.truth tptp.b))) (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule resolution :premises (t394 t395))
% 7.65/7.87  (step t397 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.b (tptp.implies tptp.truth tptp.b))) (not (= tptp.b (tptp.implies tptp.truth tptp.b)))) :rule implies_neg2)
% 7.65/7.87  (step t398 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.b (tptp.implies tptp.truth tptp.b))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.b (tptp.implies tptp.truth tptp.b)))) :rule resolution :premises (t396 t397))
% 7.65/7.87  (step t399 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.b (tptp.implies tptp.truth tptp.b)))) :rule contraction :premises (t398))
% 7.65/7.87  (step t400 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule implies :premises (t399))
% 7.65/7.87  (step t401 (cl (= tptp.b (tptp.implies tptp.truth tptp.b))) :rule resolution :premises (t400 t291))
% 7.65/7.87  (step t402 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.a (tptp.implies tptp.truth tptp.a))) (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t403)
% 7.65/7.87  (assume t403.a0 (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))))
% 7.65/7.87  (step t403.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.a (tptp.implies tptp.truth tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 7.65/7.87  (step t403.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule or :premises (t403.t1))
% 7.65/7.87  (step t403.t3 (cl (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule resolution :premises (t403.t2 t403.a0))
% 7.65/7.87  (step t403 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule subproof :discharge (t403.a0))
% 7.65/7.87  (step t404 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.a (tptp.implies tptp.truth tptp.a))) (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule resolution :premises (t402 t403))
% 7.65/7.87  (step t405 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.a (tptp.implies tptp.truth tptp.a))) (not (= tptp.a (tptp.implies tptp.truth tptp.a)))) :rule implies_neg2)
% 7.65/7.87  (step t406 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.a (tptp.implies tptp.truth tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.a (tptp.implies tptp.truth tptp.a)))) :rule resolution :premises (t404 t405))
% 7.65/7.87  (step t407 (cl (=> (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X))) (= tptp.a (tptp.implies tptp.truth tptp.a)))) :rule contraction :premises (t406))
% 7.65/7.87  (step t408 (cl (not (forall ((X $$unsorted)) (= X (tptp.implies tptp.truth X)))) (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule implies :premises (t407))
% 7.65/7.87  (step t409 (cl (= tptp.a (tptp.implies tptp.truth tptp.a))) :rule resolution :premises (t408 t291))
% 7.65/7.87  (step t410 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t411)
% 7.65/7.87  (assume t411.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.87  (step t411.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies tptp.a tptp.b)) (:= Z (tptp.implies tptp.b tptp.a))))
% 7.65/7.87  (step t411.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule or :premises (t411.t1))
% 7.65/7.87  (step t411.t3 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t411.t2 t411.a0))
% 7.65/7.87  (step t411 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule subproof :discharge (t411.a0))
% 7.65/7.87  (step t412 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t410 t411))
% 7.65/7.87  (step t413 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))))) :rule implies_neg2)
% 7.65/7.87  (step t414 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))))) :rule resolution :premises (t412 t413))
% 7.65/7.87  (step t415 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))))) :rule contraction :premises (t414))
% 7.65/7.87  (step t416 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule implies :premises (t415))
% 7.65/7.87  (step t417 (cl (= (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t416 a11))
% 7.65/7.87  (step t418 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t419)
% 7.65/7.87  (assume t419.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.87  (step t419.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))) (:= Y tptp.b) (:= Z tptp.a)))
% 7.65/7.87  (step t419.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule or :premises (t419.t1))
% 7.65/7.87  (step t419.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t419.t2 t419.a0))
% 7.65/7.87  (step t419 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule subproof :discharge (t419.a0))
% 7.65/7.87  (step t420 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t418 t419))
% 7.65/7.87  (step t421 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t422 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t420 t421))
% 7.65/7.87  (step t423 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule contraction :premises (t422))
% 7.65/7.87  (step t424 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule implies :premises (t423))
% 7.65/7.87  (step t425 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t424 a11))
% 7.65/7.87  (step t426 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t427)
% 7.65/7.87  (assume t427.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t427.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))
% 7.65/7.87  (step t427.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule or :premises (t427.t1))
% 7.65/7.87  (step t427.t3 (cl (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t427.t2 t427.a0))
% 7.65/7.87  (step t427 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule subproof :discharge (t427.a0))
% 7.65/7.87  (step t428 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t426 t427))
% 7.65/7.87  (step t429 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule implies_neg2)
% 7.65/7.87  (step t430 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule resolution :premises (t428 t429))
% 7.65/7.87  (step t431 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b))))) :rule contraction :premises (t430))
% 7.65/7.87  (step t432 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule implies :premises (t431))
% 7.65/7.87  (step t433 (cl (= tptp.truth (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) tptp.b)))) :rule resolution :premises (t432 t245))
% 7.65/7.87  (step t434 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t435)
% 7.65/7.87  (assume t435.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t435.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.b tptp.a)) (:= Y (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))))
% 7.65/7.87  (step t435.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule or :premises (t435.t1))
% 7.65/7.87  (step t435.t3 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t435.t2 t435.a0))
% 7.65/7.87  (step t435 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule subproof :discharge (t435.a0))
% 7.65/7.87  (step t436 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t434 t435))
% 7.65/7.87  (step t437 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))))) :rule implies_neg2)
% 7.65/7.87  (step t438 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))))) :rule resolution :premises (t436 t437))
% 7.65/7.87  (step t439 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)))))) :rule contraction :premises (t438))
% 7.65/7.87  (step t440 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule implies :premises (t439))
% 7.65/7.87  (step t441 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t440 t245))
% 7.65/7.87  (step t442 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t443)
% 7.65/7.87  (assume t443.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t443.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies tptp.b tptp.a))))
% 7.65/7.87  (step t443.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule or :premises (t443.t1))
% 7.65/7.87  (step t443.t3 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t443.t2 t443.a0))
% 7.65/7.87  (step t443 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule subproof :discharge (t443.a0))
% 7.65/7.87  (step t444 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t442 t443))
% 7.65/7.87  (step t445 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t446 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule resolution :premises (t444 t445))
% 7.65/7.87  (step t447 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a))))) :rule contraction :premises (t446))
% 7.65/7.87  (step t448 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule implies :premises (t447))
% 7.65/7.87  (step t449 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a)))) :rule resolution :premises (t448 t245))
% 7.65/7.87  (step t450 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t451)
% 7.65/7.87  (assume t451.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t451.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)) (:= Y tptp.a)))
% 7.65/7.87  (step t451.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule or :premises (t451.t1))
% 7.65/7.87  (step t451.t3 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t451.t2 t451.a0))
% 7.65/7.87  (step t451 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule subproof :discharge (t451.a0))
% 7.65/7.87  (step t452 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t450 t451))
% 7.65/7.87  (step t453 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule implies_neg2)
% 7.65/7.87  (step t454 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule resolution :premises (t452 t453))
% 7.65/7.87  (step t455 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))))) :rule contraction :premises (t454))
% 7.65/7.87  (step t456 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule implies :premises (t455))
% 7.65/7.87  (step t457 (cl (= tptp.truth (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t456 t245))
% 7.65/7.87  (step t458 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.a tptp.a))) (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t459)
% 7.65/7.87  (assume t459.a0 (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))))
% 7.65/7.87  (step t459.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.a tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 7.65/7.87  (step t459.t2 (cl (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule or :premises (t459.t1))
% 7.65/7.87  (step t459.t3 (cl (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule resolution :premises (t459.t2 t459.a0))
% 7.65/7.87  (step t459 (cl (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule subproof :discharge (t459.a0))
% 7.65/7.87  (step t460 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.a tptp.a))) (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule resolution :premises (t458 t459))
% 7.65/7.87  (step t461 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.a tptp.a))) (not (= tptp.truth (tptp.implies tptp.a tptp.a)))) :rule implies_neg2)
% 7.65/7.87  (step t462 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.a tptp.a))) (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.a tptp.a)))) :rule resolution :premises (t460 t461))
% 7.65/7.87  (step t463 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.a tptp.a)))) :rule contraction :premises (t462))
% 7.65/7.87  (step t464 (cl (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule implies :premises (t463))
% 7.65/7.87  (step t465 (cl (not (= (forall ((X $$unsorted)) (= (tptp.implies X X) tptp.truth)) (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))))) (not (forall ((X $$unsorted)) (= (tptp.implies X X) tptp.truth))) (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) :rule equiv_pos2)
% 7.65/7.87  (anchor :step t466 :args ((X $$unsorted) (:= X X)))
% 7.65/7.87  (step t466.t1 (cl (= X X)) :rule refl)
% 7.65/7.87  (step t466.t2 (cl (= (= (tptp.implies X X) tptp.truth) (= tptp.truth (tptp.implies X X)))) :rule all_simplify)
% 7.65/7.87  (step t466 (cl (= (forall ((X $$unsorted)) (= (tptp.implies X X) tptp.truth)) (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))))) :rule bind)
% 7.65/7.87  (step t467 (cl (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) :rule resolution :premises (t465 t466 a5))
% 7.65/7.87  (step t468 (cl (= tptp.truth (tptp.implies tptp.a tptp.a))) :rule resolution :premises (t464 t467))
% 7.65/7.87  (step t469 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.b tptp.b))) (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t470)
% 7.65/7.87  (assume t470.a0 (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))))
% 7.65/7.87  (step t470.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.b tptp.b)))) :rule forall_inst :args ((:= X tptp.b)))
% 7.65/7.87  (step t470.t2 (cl (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule or :premises (t470.t1))
% 7.65/7.87  (step t470.t3 (cl (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule resolution :premises (t470.t2 t470.a0))
% 7.65/7.87  (step t470 (cl (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule subproof :discharge (t470.a0))
% 7.65/7.87  (step t471 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.b tptp.b))) (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule resolution :premises (t469 t470))
% 7.65/7.87  (step t472 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.b tptp.b))) (not (= tptp.truth (tptp.implies tptp.b tptp.b)))) :rule implies_neg2)
% 7.65/7.87  (step t473 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.b tptp.b))) (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.b tptp.b)))) :rule resolution :premises (t471 t472))
% 7.65/7.87  (step t474 (cl (=> (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X))) (= tptp.truth (tptp.implies tptp.b tptp.b)))) :rule contraction :premises (t473))
% 7.65/7.87  (step t475 (cl (not (forall ((X $$unsorted)) (= tptp.truth (tptp.implies X X)))) (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule implies :premises (t474))
% 7.65/7.87  (step t476 (cl (= tptp.truth (tptp.implies tptp.b tptp.b))) :rule resolution :premises (t475 t467))
% 7.65/7.87  (step t477 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t478)
% 7.65/7.87  (assume t478.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.87  (step t478.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (:= Y (tptp.implies tptp.b tptp.a))))
% 7.65/7.87  (step t478.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule or :premises (t478.t1))
% 7.65/7.87  (step t478.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t478.t2 t478.a0))
% 7.65/7.87  (step t478 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule subproof :discharge (t478.a0))
% 7.65/7.87  (step t479 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t477 t478))
% 7.65/7.87  (step t480 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule implies_neg2)
% 7.65/7.87  (step t481 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule resolution :premises (t479 t480))
% 7.65/7.87  (step t482 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule contraction :premises (t481))
% 7.65/7.87  (step t483 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule implies :premises (t482))
% 7.65/7.87  (step t484 (cl (= (tptp.implies (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t483 a3))
% 7.65/7.87  (step t485 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t486)
% 7.65/7.87  (assume t486.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.87  (step t486.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule forall_inst :args ((:= X tptp.b) (:= Y tptp.a)))
% 7.65/7.87  (step t486.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule or :premises (t486.t1))
% 7.65/7.87  (step t486.t3 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule resolution :premises (t486.t2 t486.a0))
% 7.65/7.87  (step t486 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule subproof :discharge (t486.a0))
% 7.65/7.87  (step t487 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule resolution :premises (t485 t486))
% 7.65/7.87  (step t488 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (not (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule implies_neg2)
% 7.65/7.87  (step t489 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule resolution :premises (t487 t488))
% 7.65/7.87  (step t490 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b)))) :rule contraction :premises (t489))
% 7.65/7.87  (step t491 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule implies :premises (t490))
% 7.65/7.87  (step t492 (cl (= (tptp.implies (tptp.implies tptp.b tptp.a) tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) tptp.b))) :rule resolution :premises (t491 a3))
% 7.65/7.87  (step t493 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t494)
% 7.65/7.87  (assume t494.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.87  (step t494.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))) (:= Y tptp.a) (:= Z tptp.b)))
% 7.65/7.87  (step t494.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule or :premises (t494.t1))
% 7.65/7.87  (step t494.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t494.t2 t494.a0))
% 7.65/7.87  (step t494 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule subproof :discharge (t494.a0))
% 7.65/7.87  (step t495 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t493 t494))
% 7.65/7.87  (step t496 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule implies_neg2)
% 7.65/7.87  (step t497 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule resolution :premises (t495 t496))
% 7.65/7.87  (step t498 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b))))) :rule contraction :premises (t497))
% 7.65/7.87  (step t499 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule implies :premises (t498))
% 7.65/7.87  (step t500 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) tptp.b)))) :rule resolution :premises (t499 a11))
% 7.65/7.87  (step t501 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t502)
% 7.65/7.87  (assume t502.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))))
% 7.65/7.87  (step t502.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (:= Z tptp.b)))
% 7.65/7.87  (step t502.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule or :premises (t502.t1))
% 7.65/7.87  (step t502.t3 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule resolution :premises (t502.t2 t502.a0))
% 7.65/7.87  (step t502 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule subproof :discharge (t502.a0))
% 7.65/7.87  (step t503 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule resolution :premises (t501 t502))
% 7.65/7.87  (step t504 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) :rule implies_neg2)
% 7.65/7.87  (step t505 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) :rule resolution :premises (t503 t504))
% 7.65/7.87  (step t506 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))))) :rule contraction :premises (t505))
% 7.65/7.87  (step t507 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= tptp.truth (tptp.implies (tptp.implies X Y) (tptp.implies (tptp.implies Z X) (tptp.implies Z Y)))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule implies :premises (t506))
% 7.65/7.87  (step t508 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))))) :rule resolution :premises (t507 t123))
% 7.65/7.87  (step t509 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t510)
% 7.65/7.87  (assume t510.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t510.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))
% 7.65/7.87  (step t510.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule or :premises (t510.t1))
% 7.65/7.87  (step t510.t3 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t510.t2 t510.a0))
% 7.65/7.87  (step t510 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule subproof :discharge (t510.a0))
% 7.65/7.87  (step t511 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t509 t510))
% 7.65/7.87  (step t512 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t513 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t511 t512))
% 7.65/7.87  (step t514 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule contraction :premises (t513))
% 7.65/7.87  (step t515 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule implies :premises (t514))
% 7.65/7.87  (step t516 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t515 t245))
% 7.65/7.87  (step t517 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t518)
% 7.65/7.87  (assume t518.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t518.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.implies tptp.a tptp.b))))
% 7.65/7.87  (step t518.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule or :premises (t518.t1))
% 7.65/7.87  (step t518.t3 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule resolution :premises (t518.t2 t518.a0))
% 7.65/7.87  (step t518 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule subproof :discharge (t518.a0))
% 7.65/7.87  (step t519 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule resolution :premises (t517 t518))
% 7.65/7.87  (step t520 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t521 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule resolution :premises (t519 t520))
% 7.65/7.87  (step t522 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule contraction :premises (t521))
% 7.65/7.87  (step t523 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule implies :premises (t522))
% 7.65/7.87  (step t524 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule resolution :premises (t523 t245))
% 7.65/7.87  (step t525 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t526)
% 7.65/7.87  (assume t526.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t526.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.a tptp.b)) (:= Y (tptp.implies tptp.b tptp.a))))
% 7.65/7.87  (step t526.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule or :premises (t526.t1))
% 7.65/7.87  (step t526.t3 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t526.t2 t526.a0))
% 7.65/7.87  (step t526 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule subproof :discharge (t526.a0))
% 7.65/7.87  (step t527 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t525 t526))
% 7.65/7.87  (step t528 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule implies_neg2)
% 7.65/7.87  (step t529 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule resolution :premises (t527 t528))
% 7.65/7.87  (step t530 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)))))) :rule contraction :premises (t529))
% 7.65/7.87  (step t531 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule implies :premises (t530))
% 7.65/7.87  (step t532 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t531 t245))
% 7.65/7.87  (step t533 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t534)
% 7.65/7.87  (assume t534.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t534.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.a tptp.b)) (:= Y tptp.b)))
% 7.65/7.87  (step t534.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule or :premises (t534.t1))
% 7.65/7.87  (step t534.t3 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t534.t2 t534.a0))
% 7.65/7.87  (step t534 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule subproof :discharge (t534.a0))
% 7.65/7.87  (step t535 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t533 t534))
% 7.65/7.87  (step t536 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))))) :rule implies_neg2)
% 7.65/7.87  (step t537 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))))) :rule resolution :premises (t535 t536))
% 7.65/7.87  (step t538 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))))) :rule contraction :premises (t537))
% 7.65/7.87  (step t539 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule implies :premises (t538))
% 7.65/7.87  (step t540 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t539 t245))
% 7.65/7.87  (step t541 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t542)
% 7.65/7.87  (assume t542.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.87  (step t542.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))) (:= Y tptp.b) (:= Z tptp.a)))
% 7.65/7.87  (step t542.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule or :premises (t542.t1))
% 7.65/7.87  (step t542.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t542.t2 t542.a0))
% 7.65/7.87  (step t542 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule subproof :discharge (t542.a0))
% 7.65/7.87  (step t543 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t541 t542))
% 7.65/7.87  (step t544 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t545 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule resolution :premises (t543 t544))
% 7.65/7.87  (step t546 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a))))) :rule contraction :premises (t545))
% 7.65/7.87  (step t547 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule implies :premises (t546))
% 7.65/7.87  (step t548 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) tptp.a)))) :rule resolution :premises (t547 a11))
% 7.65/7.87  (step t549 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t550)
% 7.65/7.87  (assume t550.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))))
% 7.65/7.87  (step t550.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule forall_inst :args ((:= X (tptp.implies tptp.a tptp.b)) (:= Y tptp.b) (:= Z tptp.a)))
% 7.65/7.87  (step t550.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule or :premises (t550.t1))
% 7.65/7.87  (step t550.t3 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule resolution :premises (t550.t2 t550.a0))
% 7.65/7.87  (step t550 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule subproof :discharge (t550.a0))
% 7.65/7.87  (step t551 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule resolution :premises (t549 t550))
% 7.65/7.87  (step t552 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (not (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t553 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule resolution :premises (t551 t552))
% 7.65/7.87  (step t554 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z)))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a))))) :rule contraction :premises (t553))
% 7.65/7.87  (step t555 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.implies X (tptp.implies Y Z)) (tptp.implies Y (tptp.implies X Z))))) (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule implies :premises (t554))
% 7.65/7.87  (step t556 (cl (= (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b (tptp.implies (tptp.implies tptp.a tptp.b) tptp.a)))) :rule resolution :premises (t555 a11))
% 7.65/7.87  (step t557 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t558)
% 7.65/7.87  (assume t558.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t558.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule forall_inst :args ((:= X (tptp.implies tptp.b tptp.a)) (:= Y (tptp.implies tptp.a tptp.b))))
% 7.65/7.87  (step t558.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule or :premises (t558.t1))
% 7.65/7.87  (step t558.t3 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t558.t2 t558.a0))
% 7.65/7.87  (step t558 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule subproof :discharge (t558.a0))
% 7.65/7.87  (step t559 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t557 t558))
% 7.65/7.87  (step t560 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (not (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule implies_neg2)
% 7.65/7.87  (step t561 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule resolution :premises (t559 t560))
% 7.65/7.87  (step t562 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)))))) :rule contraction :premises (t561))
% 7.65/7.87  (step t563 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule implies :premises (t562))
% 7.65/7.87  (step t564 (cl (= tptp.truth (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t563 t245))
% 7.65/7.87  (step t565 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t566)
% 7.65/7.87  (assume t566.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t566.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.b)))
% 7.65/7.87  (step t566.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule or :premises (t566.t1))
% 7.65/7.87  (step t566.t3 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t566.t2 t566.a0))
% 7.65/7.87  (step t566 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule subproof :discharge (t566.a0))
% 7.65/7.87  (step t567 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t565 t566))
% 7.65/7.87  (step t568 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (not (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule implies_neg2)
% 7.65/7.87  (step t569 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule resolution :premises (t567 t568))
% 7.65/7.87  (step t570 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a))))) :rule contraction :premises (t569))
% 7.65/7.87  (step t571 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule implies :premises (t570))
% 7.65/7.87  (step t572 (cl (= tptp.truth (tptp.implies tptp.a (tptp.implies tptp.b tptp.a)))) :rule resolution :premises (t571 t245))
% 7.65/7.87  (step t573 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t574)
% 7.65/7.87  (assume t574.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))))
% 7.65/7.87  (step t574.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule forall_inst :args ((:= X tptp.b) (:= Y tptp.a)))
% 7.65/7.87  (step t574.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule or :premises (t574.t1))
% 7.65/7.87  (step t574.t3 (cl (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t574.t2 t574.a0))
% 7.65/7.87  (step t574 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule subproof :discharge (t574.a0))
% 7.65/7.87  (step t575 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t573 t574))
% 7.65/7.87  (step t576 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (not (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule implies_neg2)
% 7.65/7.87  (step t577 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t575 t576))
% 7.65/7.87  (step t578 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X)))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b))))) :rule contraction :premises (t577))
% 7.65/7.87  (step t579 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= tptp.truth (tptp.implies X (tptp.implies Y X))))) (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule implies :premises (t578))
% 7.65/7.87  (step t580 (cl (= tptp.truth (tptp.implies tptp.b (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t579 t245))
% 7.65/7.87  (step t581 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) :rule implies_neg1)
% 7.65/7.87  (anchor :step t582)
% 7.65/7.87  (assume t582.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))))
% 7.65/7.87  (step t582.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))))) :rule forall_inst :args ((:= X (tptp.implies tptp.a tptp.b)) (:= Y (tptp.implies tptp.b tptp.a))))
% 7.65/7.87  (step t582.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule or :premises (t582.t1))
% 7.65/7.87  (step t582.t3 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t582.t2 t582.a0))
% 7.65/7.87  (step t582 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule subproof :discharge (t582.a0))
% 7.65/7.87  (step t583 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t581 t582))
% 7.65/7.87  (step t584 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (not (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))))) :rule implies_neg2)
% 7.65/7.87  (step t585 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))))) :rule resolution :premises (t583 t584))
% 7.65/7.87  (step t586 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b))))) :rule contraction :premises (t585))
% 7.65/7.87  (step t587 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.implies (tptp.implies X Y) Y) (tptp.implies (tptp.implies Y X) X)))) (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule implies :premises (t586))
% 7.65/7.87  (step t588 (cl (= (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a)) (tptp.implies (tptp.implies (tptp.implies tptp.b tptp.a) (tptp.implies tptp.a tptp.b)) (tptp.implies tptp.a tptp.b)))) :rule resolution :premises (t587 a3))
% 7.65/7.87  (step t589 (cl (not (= tptp.truth (tptp.implies (tptp.implies (tptp.implies tptp.a tptp.b) (tptp.implies tptp.b tptp.a)) (tptp.implies tptp.b tptp.a))))) :rule not_symm :premises (a15))
% 7.65/7.87  (step t590 (cl) :rule resolution :premises (t73 t84 t92 t100 t113 t124 t132 t140 t148 t156 t164 t175 t183 t191 t199 t207 t215 t223 t235 t246 t257 t265 t273 t281 t292 t300 t308 t316 t324 t332 t340 t348 t361 t369 t377 t385 t393 t401 t409 t417 t425 t433 t441 t449 t457 t468 t476 t484 t492 t500 t508 t516 t524 t532 t540 t548 t556 t564 t572 t580 t588 t589))
% 7.65/7.87  
% 7.65/7.87  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.suICpS9uhI/cvc5---1.0.5_10465.smt2
% 7.65/7.88  % cvc5---1.0.5 exiting
% 7.65/7.88  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------