%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 11:48:53 AM UTC 2026
% Result : Unsatisfiable 23.87s 3.56s
% Output : CNFRefutation 25.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 3 RR)
% Number of literals : 117 ( 116 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 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 : 349 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_35) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,is_a_theorem(implies(not(X4),implies(X3,implies(X2,implies(X4,X5))))),true) = is_a_theorem(implies(not(X4),implies(X3,implies(X2,implies(X4,X5))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
is_a_theorem(implies(not(X5),implies(X4,implies(X3,implies(X5,X2))))) = ifeq(true,true,is_a_theorem(implies(not(X5),implies(X4,implies(X3,implies(X5,X2))))),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),true) = is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,is_a_theorem(implies(not(X3),implies(X3,X2))),true) = is_a_theorem(implies(not(X3),implies(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
is_a_theorem(implies(not(X3),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(not(X3),implies(X3,X2))),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
cnf(c12,plain,
is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
true = is_a_theorem(implies(X3,implies(not(X3),X2))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
ifeq(true,true,is_a_theorem(implies(not(X3),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,is_a_theorem(implies(not(X3),implies(X3,X2))),true),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,axiom,
is_a_theorem(implies(implies(X2,implies(Y2,Z)),implies(Y2,implies(X2,Z)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_21) ).
cnf(c18,plain,
is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
true = is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,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/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(c22,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = true,
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
ifeq(is_a_theorem(implies(X4,implies(X3,X2))),true,is_a_theorem(implies(X3,implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c16,c23]) ).
cnf(c25,plain,
ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,is_a_theorem(implies(not(X3),implies(X3,X2))),true) = true,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
ifeq(true,true,is_a_theorem(implies(not(X3),implies(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c14,c25]) ).
cnf(c27,plain,
is_a_theorem(implies(not(X3),implies(X3,X2))) = true,
inference(transitivity,[status(thm)],[c10,c26]) ).
cnf(c28,plain,
true = is_a_theorem(implies(not(X3),implies(X3,X2))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
ifeq(true,true,is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(not(X4),implies(X4,X2))),true,is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true),true) = ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true),true),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true) = is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,axiom,
is_a_theorem(implies(X2,implies(Y2,X2))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_18) ).
cnf(c35,plain,
is_a_theorem(implies(X3,implies(X2,X3))) = true,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
true = is_a_theorem(implies(X3,implies(X2,X3))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true) = ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),true) = ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),true),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,axiom,
is_a_theorem(implies(implies(Y2,Z2),implies(implies(X2,Y2),implies(X2,Z2)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_22) ).
cnf(c41,plain,
is_a_theorem(implies(implies(X3,implies(X2,X3)),implies(implies(X4,X3),implies(X4,implies(X2,X3))))) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
true = is_a_theorem(implies(implies(X3,implies(X2,X3)),implies(implies(X4,X3),implies(X4,implies(X2,X3))))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),true) = ifeq(is_a_theorem(implies(implies(X3,implies(X2,X3)),implies(implies(X4,X3),implies(X4,implies(X2,X3))))),true,ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),true),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(is_a_theorem(implies(implies(X3,implies(X2,X3)),implies(implies(X4,X3),implies(X4,implies(X2,X3))))),true,ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),true) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c45,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true),true) = true,
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
ifeq(is_a_theorem(implies(X3,implies(X2,X3))),true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c39,c45]) ).
cnf(c47,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c37,c46]) ).
cnf(c48,plain,
is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))) = true,
inference(transitivity,[status(thm)],[c33,c47]) ).
cnf(c49,plain,
true = is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true),true) = ifeq(is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true),true),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq(is_a_theorem(implies(implies(X4,X3),implies(X4,implies(X2,X3)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true),true) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c52,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true),true) = true,
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(X4,implies(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c31,c52]) ).
cnf(c54,plain,
ifeq(is_a_theorem(implies(not(X4),implies(X4,X2))),true,is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
ifeq(true,true,is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c29,c54]) ).
cnf(c56,plain,
is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c8,c55]) ).
cnf(c57,plain,
true = is_a_theorem(implies(not(X4),implies(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq(true,true,is_a_theorem(implies(not(X5),implies(X4,implies(X3,implies(X5,X2))))),true) = ifeq(is_a_theorem(implies(not(X5),implies(X3,implies(X5,X2)))),true,is_a_theorem(implies(not(X5),implies(X4,implies(X3,implies(X5,X2))))),true),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
ifeq(is_a_theorem(implies(not(X5),implies(X3,implies(X5,X2)))),true,is_a_theorem(implies(not(X5),implies(X4,implies(X3,implies(X5,X2))))),true) = true,
inference(substitution,[status(thm)],[c53]) ).
cnf(c60,plain,
ifeq(true,true,is_a_theorem(implies(not(X5),implies(X4,implies(X3,implies(X5,X2))))),true) = true,
inference(transitivity,[status(thm)],[c58,c59]) ).
cnf(c61,plain,
is_a_theorem(implies(not(X5),implies(X4,implies(X3,implies(X5,X2))))) = true,
inference(transitivity,[status(thm)],[c6,c60]) ).
cnf(c62,plain,
is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))) = true,
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
true = is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),true) = ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c66,plain,
ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),true),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c68,plain,
is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))) = ifeq(true,true,is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq(true,true,is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c70,plain,
is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))) = ifeq(true,true,is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true) = is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c72,plain,
is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))) = ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
is_a_theorem(implies(implies(implies(X4,X3),implies(implies(X2,X4),implies(X2,X3))),implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3)))))) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c74,plain,
true = is_a_theorem(implies(implies(implies(X4,X3),implies(implies(X2,X4),implies(X2,X3))),implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3)))))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true) = ifeq(is_a_theorem(implies(implies(implies(X4,X3),implies(implies(X2,X4),implies(X2,X3))),implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3)))))),true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c77,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4))),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
is_a_theorem(implies(implies(X4,X3),implies(implies(X2,X4),implies(X2,X3)))) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c80,plain,
true = is_a_theorem(implies(implies(X4,X3),implies(implies(X2,X4),implies(X2,X3)))),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4)))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4))),X2)),true,ifeq(is_a_theorem(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4)))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4))),X2)),true,ifeq(is_a_theorem(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4)))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c84,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X3,X5),implies(X3,X4))),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c78,c84]) ).
cnf(c86,plain,
ifeq(is_a_theorem(implies(implies(implies(X4,X3),implies(implies(X2,X4),implies(X2,X3))),implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3)))))),true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true) = true,
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true) = true,
inference(transitivity,[status(thm)],[c75,c86]) ).
cnf(c88,plain,
is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))) = true,
inference(transitivity,[status(thm)],[c72,c87]) ).
cnf(c89,plain,
true = is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(true,true,is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = ifeq(is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true,is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
ifeq(is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X5,implies(implies(X2,X4),implies(X2,X3))))),true,is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = true,
inference(substitution,[status(thm)],[c24]) ).
cnf(c92,plain,
ifeq(true,true,is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = true,
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))) = true,
inference(transitivity,[status(thm)],[c70,c92]) ).
cnf(c94,plain,
true = is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = ifeq(is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true,is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true),true) = ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c97,plain,
ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true),true),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,axiom,
is_a_theorem(implies(implies(X2,Y2),implies(implies(not(X2),Y2),Y2))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_54) ).
cnf(c99,plain,
is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X2),X2))) = true,
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
true = is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X2),X2))),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true),true) = ifeq(is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X2),X2))),true,ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true),true),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
ifeq(is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X2),X2))),true,ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true),true) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c103,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
ifeq(is_a_theorem(implies(X3,X2)),true,is_a_theorem(implies(implies(not(X3),X2),X2)),true) = true,
inference(transitivity,[status(thm)],[c97,c103]) ).
cnf(c105,plain,
ifeq(is_a_theorem(implies(X5,implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true,is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = true,
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))),true) = true,
inference(transitivity,[status(thm)],[c95,c105]) ).
cnf(c107,plain,
is_a_theorem(implies(implies(not(X5),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3)))),implies(implies(X5,implies(X4,X3)),implies(implies(X2,X4),implies(X2,X3))))) = true,
inference(transitivity,[status(thm)],[c68,c106]) ).
cnf(c108,plain,
is_a_theorem(implies(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))) = true,
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
true = is_a_theorem(implies(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),true) = ifeq(is_a_theorem(implies(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),true),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
ifeq(is_a_theorem(implies(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),true) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c112,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true),true) = true,
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
ifeq(is_a_theorem(implies(not(X4),implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c66,c112]) ).
cnf(c114,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c64,c113]) ).
cnf(c115,plain,
is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(implies(X4,X3),implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c4,c114]) ).
cnf(c116,plain,
is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) = true,
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
$false,
inference(resolution,[status(thm)],[c1,c116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n007.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 15:16:39 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.87/3.56 Command-line arguments: --flatten-regeneralise
% 23.87/3.56
% 23.87/3.56 % SZS status Unsatisfiable
% 23.87/3.56
% 23.87/3.57 % SZS output start CNFRefutation
% See solution above
% 25.44/3.73
% 25.44/3.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------