%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL443-10 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:40:23 PM UTC 2026
% Result : Unsatisfiable 1.38s 1.77s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 8 RR)
% Number of literals : 26 ( 25 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 53 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_PropLog_Othms_OH_0,axiom,
ifeq(c_in(X1,X2,tc_PropLog_Opl(X3)),true,c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(cls_PropLog_Oweaken__left__insert_0,axiom,
ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(X1,c_PropLog_Othms(c_insert(X4,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
cnf(cls_conjecture_1,negated_conjecture,
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',cls_conjecture_1) ).
cnf(cls_PropLog_Othms_OMP_0,axiom,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),true,ifeq(c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),true,c_in(X2,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_PropLog_Odeduction_0,axiom,
ifeq(c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,X4),c_PropLog_Othms(X3,X4),tc_PropLog_Opl(X4)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
cnf(cls_conjecture_2,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(c_0_9,axiom,
ifeq(c_in(X1,X2,tc_PropLog_Opl(X3)),true,c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true) = true,
cls_PropLog_Othms_OH_0 ).
cnf(c_0_10,axiom,
c_in(X1,c_insert(X1,X2,X3),X3) = true,
cls_Set_OinsertCI_1 ).
cnf(c_0_11,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_12,axiom,
ifeq(c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)),true,c_in(X1,c_PropLog_Othms(c_insert(X4,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true) = true,
cls_PropLog_Oweaken__left__insert_0 ).
cnf(c_0_13,negated_conjecture,
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,
cls_conjecture_1 ).
cnf(c_0_14,axiom,
ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),true,ifeq(c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),true,c_in(X2,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),true),true) = true,
cls_PropLog_Othms_OMP_0 ).
cnf(c_0_15,plain,
c_in(X1,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_16,negated_conjecture,
c_in(v_p,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) = true,
cls_conjecture_0 ).
cnf(c_0_17,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_q,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]) ).
cnf(c_0_18,plain,
ifeq(c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true,c_in(X2,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_11]) ).
cnf(c_0_19,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_insert(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_11]) ).
cnf(c_0_20,negated_conjecture,
ifeq(c_in(v_q,c_PropLog_Othms(c_insert(X1,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(X1,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_11]) ).
cnf(c_0_21,negated_conjecture,
c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,X1,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_11]) ).
cnf(c_0_22,axiom,
ifeq(c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),true,c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,X4),c_PropLog_Othms(X3,X4),tc_PropLog_Opl(X4)),true) = true,
cls_PropLog_Odeduction_0 ).
cnf(c_0_23,negated_conjecture,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_11]) ).
cnf(c_0_24,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,
cls_conjecture_2 ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_11]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL443-10 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 22:35:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.38/1.77 % Version : CSE_E---1.7
% 1.38/1.77 % Problem : theBenchmark.p
% 1.38/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.38/1.77 % SZS output start CNFRefutation
% See solution above
% 1.38/1.77 % Total time : 1.371s
%------------------------------------------------------------------------------