%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL384-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:43 AM UTC 2026
% Result : Unsatisfiable 102.91s 13.50s
% Output : CNFRefutation 105.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 6
% Syntax : Number of clauses : 197 ( 197 unt; 0 nHn; 3 RR)
% Number of literals : 197 ( 196 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 564 ( 59 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_45) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))),true) = is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))),true) = is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))) = ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))),true) = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))),true) = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))),true),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X4),X4),X4)),X3),X2),implies(not(X2),X5))),true) = is_a_theorem(implies(implies(implies(not(implies(implies(not(X4),X4),X4)),X3),X2),implies(not(X2),X5))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2))),true),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))),true) = is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))) = ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))),true),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))),true) = is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))),true),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))),true) = is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))) = ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))),true),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))),true) = is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))) = ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))),true),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)),true) = is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)) = ifeq(true,true,is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)),true),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
is_a_theorem(implies(implies(not(X2),X2),X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c26,plain,
true = is_a_theorem(implies(implies(not(X2),X2),X2)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)),true) = ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)),true),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
cnf(c31,plain,
is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
true = is_a_theorem(implies(X3,implies(not(X3),X2))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
ifeq(is_a_theorem(implies(X2,Y2)),true,ifeq(is_a_theorem(X2),true,is_a_theorem(Y2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(c35,plain,
ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true) = true,
inference(transitivity,[status(thm)],[c29,c36]) ).
cnf(c38,plain,
ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)),true) = true,
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)),true) = true,
inference(transitivity,[status(thm)],[c27,c38]) ).
cnf(c40,plain,
is_a_theorem(implies(not(implies(implies(not(X3),X3),X3)),X2)) = true,
inference(transitivity,[status(thm)],[c24,c39]) ).
cnf(c41,plain,
is_a_theorem(implies(not(implies(implies(not(X2),X2),X2)),X3)) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
true = is_a_theorem(implies(not(implies(implies(not(X2),X2),X2)),X3)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))),true) = ifeq(is_a_theorem(implies(not(implies(implies(not(X2),X2),X2)),X4)),true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))),true),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,axiom,
is_a_theorem(implies(implies(X2,Y2),implies(implies(Y2,Z),implies(X2,Z)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
cnf(c47,plain,
is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
true = is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c51,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(transitivity,[status(thm)],[c49,c50]) ).
cnf(c52,plain,
ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c45,c51]) ).
cnf(c53,plain,
ifeq(is_a_theorem(implies(not(implies(implies(not(X2),X2),X2)),X4)),true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))),true) = true,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))),true) = true,
inference(transitivity,[status(thm)],[c43,c53]) ).
cnf(c55,plain,
is_a_theorem(implies(implies(X4,X3),implies(not(implies(implies(not(X2),X2),X2)),X3))) = true,
inference(transitivity,[status(thm)],[c22,c54]) ).
cnf(c56,plain,
is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(implies(not(X3),X3),X3)),X2))) = true,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
true = is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(implies(not(X3),X3),X3)),X2))),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(implies(not(X3),X3),X3)),X2))),true,is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))),true),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c60,plain,
ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c64,plain,
true = is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
inference(substitution,[status(thm)],[c30]) ).
cnf(c70,plain,
true = is_a_theorem(implies(X3,implies(not(X3),X2))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c74,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c68,c74]) ).
cnf(c76,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = true,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c65,c76]) ).
cnf(c78,plain,
is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))) = true,
inference(transitivity,[status(thm)],[c62,c77]) ).
cnf(c79,plain,
true = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c82,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = true,
inference(transitivity,[status(thm)],[c60,c82]) ).
cnf(c84,plain,
ifeq(is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(implies(not(X3),X3),X3)),X2))),true,is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))),true) = true,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))),true) = true,
inference(transitivity,[status(thm)],[c58,c84]) ).
cnf(c86,plain,
is_a_theorem(implies(X4,implies(not(implies(implies(not(X3),X3),X3)),X2))) = true,
inference(transitivity,[status(thm)],[c20,c85]) ).
cnf(c87,plain,
is_a_theorem(implies(X2,implies(not(implies(implies(not(X4),X4),X4)),X3))) = true,
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
true = is_a_theorem(implies(X2,implies(not(implies(implies(not(X4),X4),X4)),X3))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))),true) = ifeq(is_a_theorem(implies(X2,implies(not(implies(implies(not(X5),X5),X5)),X4))),true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))),true),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(is_a_theorem(implies(X2,implies(not(implies(implies(not(X5),X5),X5)),X4))),true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c52]) ).
cnf(c91,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(X2,X3))) = true,
inference(transitivity,[status(thm)],[c18,c91]) ).
cnf(c93,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X4),implies(not(X4),X4))) = true,
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
true = is_a_theorem(implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X4),implies(not(X4),X4))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),implies(not(X5),X5))),true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))),true),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c97,plain,
ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c99,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c101,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c103,plain,
is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c105,plain,
true = is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c108,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
true = is_a_theorem(implies(implies(not(X2),X2),X2)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c111,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c114,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c109,c114]) ).
cnf(c116,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = true,
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c106,c116]) ).
cnf(c118,plain,
is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))) = true,
inference(transitivity,[status(thm)],[c103,c117]) ).
cnf(c119,plain,
true = is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(not(X4),X4),X3))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(not(X4),X4),X3))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = true,
inference(substitution,[status(thm)],[c52]) ).
cnf(c122,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))) = true,
inference(transitivity,[status(thm)],[c101,c122]) ).
cnf(c124,plain,
is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
true = is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c128,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c130,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
is_a_theorem(implies(implies(X2,X4),implies(implies(X4,X3),implies(X2,X3)))) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c132,plain,
true = is_a_theorem(implies(implies(X2,X4),implies(implies(X4,X3),implies(X2,X3)))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = ifeq(is_a_theorem(implies(implies(X3,X5),implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
ifeq(is_a_theorem(implies(implies(X3,X5),implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = true,
inference(substitution,[status(thm)],[c52]) ).
cnf(c135,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = true,
inference(transitivity,[status(thm)],[c133,c134]) ).
cnf(c136,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))) = true,
inference(transitivity,[status(thm)],[c130,c135]) ).
cnf(c137,plain,
true = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c140,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true) = true,
inference(transitivity,[status(thm)],[c128,c140]) ).
cnf(c142,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c126,c142]) ).
cnf(c144,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c99,c143]) ).
cnf(c145,plain,
true = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c148,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(transitivity,[status(thm)],[c146,c147]) ).
cnf(c149,plain,
ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c97,c148]) ).
cnf(c150,plain,
ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),implies(not(X5),X5))),true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))),true) = true,
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))),true) = true,
inference(transitivity,[status(thm)],[c95,c150]) ).
cnf(c152,plain,
is_a_theorem(implies(implies(X5,X4),implies(implies(implies(not(implies(implies(not(X3),X3),X3)),X2),X5),X4))) = true,
inference(transitivity,[status(thm)],[c16,c151]) ).
cnf(c153,plain,
is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2)))) = true,
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
true = is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2)))),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2))),true) = ifeq(is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2)))),true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2))),true),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
ifeq(is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2)))),true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2))),true) = true,
inference(substitution,[status(thm)],[c75]) ).
cnf(c157,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c155,c156]) ).
cnf(c158,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X5),X5),X5)),X4),X3),implies(not(X3),X2))) = true,
inference(transitivity,[status(thm)],[c14,c157]) ).
cnf(c159,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X4),X4),X4)),implies(implies(not(X4),X4),X4)),X3),implies(not(X3),X2))) = true,
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
true = is_a_theorem(implies(implies(implies(not(implies(implies(not(X4),X4),X4)),implies(implies(not(X4),X4),X4)),X3),implies(not(X3),X2))),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(X4),X4),X4)),implies(implies(not(X4),X4),X4)),X3),implies(not(X3),X2))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))),true),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c163,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
true = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c165,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c167,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true) = true,
inference(transitivity,[status(thm)],[c163,c167]) ).
cnf(c169,plain,
ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(X4),X4),X4)),implies(implies(not(X4),X4),X4)),X3),implies(not(X3),X2))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))),true) = true,
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c161,c169]) ).
cnf(c171,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(not(X3),X2))) = true,
inference(transitivity,[status(thm)],[c12,c170]) ).
cnf(c172,plain,
is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(not(implies(X4,X3)),X2))) = true,
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
true = is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(not(implies(X4,X3)),X2))),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(not(implies(X4,X3)),X2))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))),true),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(not(implies(X4,X3)),X2))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))),true) = true,
inference(substitution,[status(thm)],[c141]) ).
cnf(c176,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))),true) = true,
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(not(implies(X4,X3)),X2))) = true,
inference(transitivity,[status(thm)],[c10,c176]) ).
cnf(c178,plain,
is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(not(implies(implies(X3,X4),X4)),X2))) = true,
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
true = is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(not(implies(implies(X3,X4),X4)),X2))),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(not(implies(implies(X3,X4),X4)),X2))),true,is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))),true),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
ifeq(is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(not(implies(implies(X3,X4),X4)),X2))),true,is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))),true) = true,
inference(substitution,[status(thm)],[c141]) ).
cnf(c182,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))),true) = true,
inference(transitivity,[status(thm)],[c180,c181]) ).
cnf(c183,plain,
is_a_theorem(implies(implies(not(X4),X3),implies(not(implies(implies(X3,X4),X4)),X2))) = true,
inference(transitivity,[status(thm)],[c8,c182]) ).
cnf(c184,plain,
is_a_theorem(implies(implies(not(X2),X3),implies(not(implies(implies(X3,X2),X2)),implies(implies(X3,X2),X2)))) = true,
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
true = is_a_theorem(implies(implies(not(X2),X3),implies(not(implies(implies(X3,X2),X2)),implies(implies(X3,X2),X2)))),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X3),X4),implies(not(implies(implies(X4,X3),X3)),implies(implies(X4,X3),X3)))),true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))),true),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
ifeq(is_a_theorem(implies(implies(not(X3),X4),implies(not(implies(implies(X4,X3),X3)),implies(implies(X4,X3),X3)))),true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))),true) = true,
inference(substitution,[status(thm)],[c149]) ).
cnf(c188,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))),true) = true,
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(implies(not(X3),X4),X2))) = true,
inference(transitivity,[status(thm)],[c6,c188]) ).
cnf(c190,plain,
is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(implies(not(X2),X3),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
true = is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c141]) ).
cnf(c194,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(not(X2),X3),implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c4,c194]) ).
cnf(c196,plain,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))) = true,
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
$false,
inference(resolution,[status(thm)],[c1,c196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL384-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 15:38:21 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 102.91/13.50 Command-line arguments: --no-flatten-goal
% 102.91/13.50
% 102.91/13.50 % SZS status Unsatisfiable
% 102.91/13.50
% 103.71/13.52 % SZS output start CNFRefutation
% See solution above
% 105.32/13.78
% 105.32/13.78 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------