%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 : Thu Sep 24 01:12:43 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.57s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 49 ( 0 equ; 24 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 : 82 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_PropLog_ODiff__weaken__left_0,axiom,
( ~ c_lessequals(X2,X5,tc_set(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_in(X1,c_PropLog_Othms(c_minus(X5,X3,tc_set(tc_PropLog_Opl(X4))),X4),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_Oweaken__left_0,axiom,
( ~ c_lessequals(X2,X4,tc_set(tc_PropLog_Opl(X3)))
| ~ c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left_0) ).
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_Othms__excluded__middle__rule_0,axiom,
( ~ 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))
| ~ 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(X3,X4),tc_PropLog_Opl(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms__excluded__middle__rule_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_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,plain,
( ~ c_lessequals(X2,X5,tc_set(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_in(X1,c_PropLog_Othms(c_minus(X5,X3,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4)) ),
inference(fof_simplification,[status(thm)],[cls_PropLog_ODiff__weaken__left_0]) ).
cnf(c_0_9,plain,
( ~ c_lessequals(X2,X5,tc_set(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_in(X1,c_PropLog_Othms(c_minus(X5,X3,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4)) ),
c_0_8 ).
cnf(c_0_10,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_11,plain,
( ~ c_lessequals(X2,X4,tc_set(tc_PropLog_Opl(X3)))
| ~ c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) ),
inference(fof_simplification,[status(thm)],[cls_PropLog_Oweaken__left_0]) ).
cnf(c_0_12,negated_conjecture,
( ~ c_lessequals(c_PropLog_Ohyps(v_p,X2,t_a),X1,tc_set(tc_PropLog_Opl(t_a)))
| 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)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,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_14,plain,
( ~ c_lessequals(X2,X4,tc_set(tc_PropLog_Opl(X3)))
| ~ c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| c_in(X1,c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)) ),
c_0_11 ).
cnf(c_0_15,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_12,c_0_13]) ).
cnf(c_0_16,plain,
( ~ 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))
| ~ 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(X3,X4),tc_PropLog_Opl(X4)) ),
inference(fof_simplification,[status(thm)],[cls_PropLog_Othms__excluded__middle__rule_0]) ).
cnf(c_0_17,negated_conjecture,
( ~ 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)))
| c_in(v_p,c_PropLog_Othms(X1,t_a),tc_PropLog_Opl(t_a)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,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_19,negated_conjecture,
( ~ 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)))
| c_in(v_p,c_PropLog_Othms(X1,t_a),tc_PropLog_Opl(t_a)) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_20,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_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)),
inference(fof_simplification,[status(thm)],[cls_conjecture_5]) ).
cnf(c_0_22,plain,
( ~ 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))
| ~ 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(X3,X4),tc_PropLog_Opl(X4)) ),
c_0_16 ).
cnf(c_0_23,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_17,c_0_18]) ).
cnf(c_0_24,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_19,c_0_20]) ).
cnf(c_0_25,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)),
c_0_21 ).
cnf(c_0_26,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_22,c_0_23]),c_0_24])]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n002.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 00:34:18 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.51 Running first-order theorem proving
% 0.18/0.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.57 % Version: 3.5.1
% 0.22/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.57 % Starting sh5l with 300s (1) cores
% 0.22/0.57 % new_bool_1 with pid 2069589 completed with status 0
% 0.22/0.57 % Result found by new_bool_1
% 0.22/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FHUNM-FFMF32-MFFFFFNN
% 0.22/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.57 % SubtermCWHack with pid 2069595 completed with status 0
% 0.22/0.57 % Result found by SubtermCWHack
% 0.22/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FHUNM-FFMF32-MFFFFFNN
% 0.22/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.57 % Preprocessing time : 0.002 s
% 0.22/0.57
% 0.22/0.57 % Proof found!
% 0.22/0.57 % SZS status Unsatisfiable
% 0.22/0.57 % SZS output start CNFRefutation
% See solution above
% 0.22/0.57 % Parsed axioms : 8
% 0.22/0.57 % Removed by relevancy pruning/SinE : 0
% 0.22/0.57 % Initial clauses : 8
% 0.22/0.57 % Removed in clause preprocessing : 0
% 0.22/0.57 % Initial clauses in saturation : 8
% 0.22/0.57 % Processed clauses : 16
% 0.22/0.57 % ...of these trivial : 0
% 0.22/0.57 % ...subsumed : 0
% 0.22/0.57 % ...remaining for further processing : 16
% 0.22/0.57 % Other redundant clauses eliminated : 0
% 0.22/0.57 % Clauses deleted for lack of memory : 0
% 0.22/0.57 % Backward-subsumed : 0
% 0.22/0.57 % Backward-rewritten : 1
% 0.22/0.57 % Generated clauses : 14
% 0.22/0.57 % ...of the previous two non-redundant : 12
% 0.22/0.57 % ...aggressively subsumed : 0
% 0.22/0.57 % Contextual simplify-reflections : 0
% 0.22/0.57 % Paramodulations : 14
% 0.22/0.57 % Factorizations : 0
% 0.22/0.57 % NegExts : 0
% 0.22/0.57 % Equation resolutions : 0
% 0.22/0.57 % Disequality decompositions : 0
% 0.22/0.57 % Total rewrite steps : 2
% 0.22/0.57 % ...of those cached : 0
% 0.22/0.57 % Propositional unsat checks : 0
% 0.22/0.57 % Propositional check models : 0
% 0.22/0.57 % Propositional check unsatisfiable : 0
% 0.22/0.57 % Propositional clauses : 0
% 0.22/0.57 % Propositional clauses after purity: 0
% 0.22/0.57 % Propositional unsat core size : 0
% 0.22/0.57 % Propositional preprocessing time : 0.000
% 0.22/0.57 % Propositional encoding time : 0.000
% 0.22/0.57 % Propositional solver time : 0.000
% 0.22/0.57 % Success case prop preproc time : 0.000
% 0.22/0.57 % Success case prop encoding time : 0.000
% 0.22/0.57 % Success case prop solver time : 0.000
% 0.22/0.57 % Current number of processed clauses : 15
% 0.22/0.57 % Positive orientable unit clauses : 8
% 0.22/0.57 % Positive unorientable unit clauses: 0
% 0.22/0.57 % Negative unit clauses : 0
% 0.22/0.57 % Non-unit-clauses : 7
% 0.22/0.57 % Current number of unprocessed clauses: 4
% 0.22/0.57 % ...number of literals in the above : 7
% 0.22/0.57 % Current number of archived formulas : 0
% 0.22/0.57 % Current number of archived clauses : 1
% 0.22/0.57 % Clause-clause subsumption calls (NU) : 4
% 0.22/0.57 % Rec. Clause-clause subsumption calls : 4
% 0.22/0.57 % Non-unit clause-clause subsumptions : 0
% 0.22/0.57 % Unit Clause-clause subsumption calls : 0
% 0.22/0.57 % Rewrite failures with RHS unbound : 0
% 0.22/0.57 % BW rewrite match attempts : 8
% 0.22/0.57 % BW rewrite match successes : 1
% 0.22/0.57 % Condensation attempts : 0
% 0.22/0.57 % Condensation successes : 0
% 0.22/0.57 % Termbank termtop insertions : 1244
% 0.22/0.57 % Search garbage collected termcells : 20
% 0.22/0.57
% 0.22/0.57 % -------------------------------------------------
% 0.22/0.57 % User time : 0.008 s
% 0.22/0.57 % System time : 0.003 s
% 0.22/0.57 % Total time : 0.010 s
% 0.22/0.57 % Maximum resident set size: 3644 pages
% 0.22/0.57
% 0.22/0.57 % -------------------------------------------------
% 0.22/0.57 % User time : 0.010 s
% 0.22/0.57 % System time : 0.010 s
% 0.22/0.57 % Total time : 0.019 s
% 0.22/0.57 % Maximum resident set size: 4608 pages
% 0.22/0.57 % E exiting
%------------------------------------------------------------------------------