%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL429-2 : TPTP v9.2.1. Released v3.2.0.
% 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 : n003.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 04:40:19 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.73s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 15 unt; 0 nHn; 12 RR)
% Number of literals : 39 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 69 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_PropLog_ODiff__weaken__left_0,axiom,
( c_in(X1,c_PropLog_Othms(c_minus(X5,X3,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_minus(X2,X3,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4))
| ~ c_lessequals(X2,X5,tc_set(tc_PropLog_Opl(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_ODiff__weaken__left_0) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X1,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_PropLog_Ohyps__Diff_0,axiom,
c_lessequals(c_PropLog_Ohyps(X1,c_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(X4)),X4),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X3,X4),c_PropLog_Opl_Ofalse,X4),c_minus(c_PropLog_Ohyps(X1,X2,X4),c_insert(c_PropLog_Opl_Ovar(X3,X4),c_emptyset,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Ohyps__Diff_0) ).
cnf(cls_PropLog_Oweaken__left_0,axiom,
( c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3))
| ~ c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_lessequals(X2,X4,tc_set(tc_PropLog_Opl(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left_0) ).
cnf(cls_PropLog_Oinsert__Diff__subset2_0,axiom,
c_lessequals(c_minus(c_insert(X1,c_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(X4)),X4),X5,tc_set(X4)),c_insert(X1,c_minus(X2,c_insert(X3,X5,X4),tc_set(X4)),X4),tc_set(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__subset2_0) ).
cnf(cls_PropLog_Oinsert__Diff__same_0,axiom,
c_lessequals(c_minus(X1,X2,tc_set(X3)),c_insert(X4,c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),X3),tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__same_0) ).
cnf(cls_PropLog_Othms__excluded__middle__rule_0,axiom,
( c_in(X1,c_PropLog_Othms(X3,X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X4),X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms__excluded__middle__rule_0) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(c_0_8,axiom,
( c_in(X1,c_PropLog_Othms(c_minus(X5,X3,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_minus(X2,X3,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4))
| ~ c_lessequals(X2,X5,tc_set(tc_PropLog_Opl(X4))) ),
cls_PropLog_ODiff__weaken__left_0 ).
cnf(c_0_9,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X1,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
cls_conjecture_3 ).
cnf(c_0_10,negated_conjecture,
( c_in(v_p,c_PropLog_Othms(c_minus(X1,v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_PropLog_Ohyps(v_p,X2,t_a),X1,tc_set(tc_PropLog_Opl(t_a))) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
c_lessequals(c_PropLog_Ohyps(X1,c_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(X4)),X4),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X3,X4),c_PropLog_Opl_Ofalse,X4),c_minus(c_PropLog_Ohyps(X1,X2,X4),c_insert(c_PropLog_Opl_Ovar(X3,X4),c_emptyset,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),
cls_PropLog_Ohyps__Diff_0 ).
cnf(c_0_12,axiom,
( c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3))
| ~ c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_lessequals(X2,X4,tc_set(tc_PropLog_Opl(X3))) ),
cls_PropLog_Oweaken__left_0 ).
cnf(c_0_13,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X1,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,X2,t_a),c_insert(c_PropLog_Opl_Ovar(X1,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( c_in(v_p,c_PropLog_Othms(X1,t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_minus(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X2,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,X3,t_a),c_insert(c_PropLog_Opl_Ovar(X2,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),X1,tc_set(tc_PropLog_Opl(t_a))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
c_lessequals(c_minus(c_insert(X1,c_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(X4)),X4),X5,tc_set(X4)),c_insert(X1,c_minus(X2,c_insert(X3,X5,X4),tc_set(X4)),X4),tc_set(X4)),
cls_PropLog_Oinsert__Diff__subset2_0 ).
cnf(c_0_16,negated_conjecture,
( c_in(v_p,c_PropLog_Othms(X1,t_a),tc_PropLog_Opl(t_a))
| ~ c_lessequals(c_minus(c_PropLog_Ohyps(v_p,X2,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),X1,tc_set(tc_PropLog_Opl(t_a))) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_17,axiom,
c_lessequals(c_minus(X1,X2,tc_set(X3)),c_insert(X4,c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),X3),tc_set(X3)),
cls_PropLog_Oinsert__Diff__same_0 ).
cnf(c_0_18,axiom,
( c_in(X1,c_PropLog_Othms(X3,X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X4),X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
cls_PropLog_Othms__excluded__middle__rule_0 ).
cnf(c_0_19,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X1,t_a),c_PropLog_Opl_Ofalse,t_a),c_minus(c_PropLog_Ohyps(v_p,X2,t_a),c_insert(c_PropLog_Opl_Ovar(X1,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_insert(X1,c_minus(c_PropLog_Ohyps(v_p,X2,t_a),c_insert(X1,v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Ovar(v_v,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
cls_conjecture_5 ).
cnf(c_0_22,negated_conjecture,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X1,t_a),c_insert(c_PropLog_Opl_Ovar(X2,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL429-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.17/0.33 % Computer : n003.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 22:33:26 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.26/1.73 % Version : CSE_E---1.7
% 1.26/1.73 % Problem : theBenchmark.p
% 1.26/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.73 % SZS output start CNFRefutation
% See solution above
% 1.26/1.73 % Total time : 1.375s
%------------------------------------------------------------------------------