%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 11:49:53 AM UTC 2026
% Result : Unsatisfiable 1.71s 0.71s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 21 RR)
% Number of literals : 70 ( 69 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 104 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = ifeq(true,true,c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
true = c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = ifeq(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
ifeq(c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)),true,c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
cnf(c15,plain,
ifeq(c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
ifeq(true,true,c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
c_in(v_p,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(transitivity,[status(thm)],[c10,c16]) ).
cnf(c18,plain,
c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
true = c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(true,true,c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = ifeq(c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,ifeq(c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X,X4,X3),X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true,c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X,X4,X3),X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true),true) = ifeq(c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X,X4,X3),X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true,c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X,X4,X3),X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
ifeq(c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = ifeq(true,true,ifeq(c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),true),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq(true,true,c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)),true) = c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)) = ifeq(true,true,c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)),true),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a2),T_a2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(c26,plain,
c_in(X3,c_insert(X3,X2,tc_PropLog_Opl(X)),tc_PropLog_Opl(X)) = true,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
true = c_in(X3,c_insert(X3,X2,tc_PropLog_Opl(X)),tc_PropLog_Opl(X)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(true,true,c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)),true) = ifeq(c_in(X3,c_insert(X3,X2,tc_PropLog_Opl(X)),tc_PropLog_Opl(X)),true,c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)),true),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
ifeq(c_in(V_p2,V_H,tc_PropLog_Opl(T_a2)),true,c_in(V_p2,c_PropLog_Othms(V_H,T_a2),tc_PropLog_Opl(T_a2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
cnf(c30,plain,
ifeq(c_in(X3,c_insert(X3,X2,tc_PropLog_Opl(X)),tc_PropLog_Opl(X)),true,c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)),true) = true,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(true,true,c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)),true) = true,
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
c_in(X3,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X)),X),tc_PropLog_Opl(X)) = true,
inference(transitivity,[status(thm)],[c24,c31]) ).
cnf(c33,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
true = c_in(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
ifeq(true,true,ifeq(c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),true) = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),true),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(V_p2,V_q,T_a2),c_PropLog_Othms(V_H2,T_a2),tc_PropLog_Opl(T_a2)),true,ifeq(c_in(V_p2,c_PropLog_Othms(V_H2,T_a2),tc_PropLog_Opl(T_a2)),true,c_in(V_q,c_PropLog_Othms(V_H2,T_a2),tc_PropLog_Opl(T_a2)),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
cnf(c37,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq(true,true,ifeq(c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true),true) = true,
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
ifeq(c_in(X4,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X3,X2),X,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = true,
inference(transitivity,[status(thm)],[c22,c38]) ).
cnf(c40,plain,
ifeq(c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
ifeq(true,true,c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(transitivity,[status(thm)],[c20,c40]) ).
cnf(c42,plain,
c_in(X,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(transitivity,[status(thm)],[c8,c41]) ).
cnf(c43,plain,
c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
true = c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = ifeq(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c51,plain,
true = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c54,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(transitivity,[status(thm)],[c49,c54]) ).
cnf(c56,plain,
true = c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c59,plain,
ifeq(true,true,ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true),true) = true,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(X,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(transitivity,[status(thm)],[c47,c59]) ).
cnf(c61,plain,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(transitivity,[status(thm)],[c45,c61]) ).
cnf(c63,plain,
c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(transitivity,[status(thm)],[c6,c62]) ).
cnf(c64,plain,
true = c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = ifeq(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,axiom,
ifeq(c_in(V_q2,c_PropLog_Othms(c_insert(V_p2,V_H2,tc_PropLog_Opl(T_a2)),T_a2),tc_PropLog_Opl(T_a2)),true,c_in(c_PropLog_Opl_Oop_A_N_62(V_p2,V_q2,T_a2),c_PropLog_Othms(V_H2,T_a2),tc_PropLog_Opl(T_a2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
cnf(c67,plain,
ifeq(c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
ifeq(true,true,c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
inference(transitivity,[status(thm)],[c4,c68]) ).
cnf(c70,plain,
$false,
inference(resolution,[status(thm)],[c1,c69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:44:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.71/0.71 Command-line arguments: --no-flatten-goal
% 1.71/0.71
% 1.71/0.71 % SZS status Unsatisfiable
% 1.71/0.71
% 1.71/0.72 % SZS output start CNFRefutation
% See solution above
% 2.44/0.78
% 2.44/0.78 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------