%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET807+4 : 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 : n008.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 02:15:26 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 46 ( 4 avg)
% Number of connectives : 128 ( 39 ~; 62 |; 20 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 1 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(rel_subset,hypothesis,
! [X3,X5] :
( apply(subset_predicate,X3,X5)
<=> subset(X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_subset) ).
fof(pre_order,axiom,
! [X7,X4] :
( pre_order(X7,X4)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X4)
& member(X5,X4)
& member(X3,X4) )
=> ( ( apply(X7,X5,X6)
& apply(X7,X3,X5) )
=> apply(X7,X3,X6) ) )
& ! [X3] :
( member(X3,X4)
=> apply(X7,X3,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',pre_order) ).
fof(thIV18a,conjecture,
! [X4] : pre_order(subset_predicate,power_set(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV18a) ).
fof(c_0_4,plain,
! [X11,X12,X13,X14,X15] :
( ( subset(X14,X15)
| ~ member(esk2_2(X14,X15),X15) )
& ( subset(X14,X15)
| member(esk2_2(X14,X15),X14) )
& ( member(X13,X12)
| ~ member(X13,X11)
| ~ subset(X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])])]) ).
fof(c_0_5,hypothesis,
! [X8,X9] :
( ( apply(subset_predicate,X8,X9)
| ~ subset(X8,X9) )
& ( subset(X8,X9)
| ~ apply(subset_predicate,X8,X9) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_subset])])]) ).
cnf(c_0_6,plain,
( ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,hypothesis,
( ~ apply(subset_predicate,X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,plain,
! [X17,X18,X19,X20,X21,X22,X23,X24] :
( ( pre_order(X23,X24)
| ~ apply(X23,esk3_2(X23,X24),esk3_2(X23,X24))
| ~ apply(X23,esk4_2(X23,X24),esk6_2(X23,X24)) )
& ( pre_order(X23,X24)
| ~ apply(X23,esk3_2(X23,X24),esk3_2(X23,X24))
| apply(X23,esk5_2(X23,X24),esk6_2(X23,X24)) )
& ( pre_order(X23,X24)
| ~ apply(X23,esk3_2(X23,X24),esk3_2(X23,X24))
| apply(X23,esk4_2(X23,X24),esk5_2(X23,X24)) )
& ( pre_order(X23,X24)
| ~ apply(X23,esk3_2(X23,X24),esk3_2(X23,X24))
| member(esk6_2(X23,X24),X24) )
& ( pre_order(X23,X24)
| ~ apply(X23,esk3_2(X23,X24),esk3_2(X23,X24))
| member(esk5_2(X23,X24),X24) )
& ( pre_order(X23,X24)
| ~ apply(X23,esk3_2(X23,X24),esk3_2(X23,X24))
| member(esk4_2(X23,X24),X24) )
& ( pre_order(X23,X24)
| member(esk3_2(X23,X24),X24)
| ~ apply(X23,esk4_2(X23,X24),esk6_2(X23,X24)) )
& ( pre_order(X23,X24)
| member(esk3_2(X23,X24),X24)
| apply(X23,esk5_2(X23,X24),esk6_2(X23,X24)) )
& ( pre_order(X23,X24)
| member(esk3_2(X23,X24),X24)
| apply(X23,esk4_2(X23,X24),esk5_2(X23,X24)) )
& ( pre_order(X23,X24)
| member(esk3_2(X23,X24),X24)
| member(esk6_2(X23,X24),X24) )
& ( pre_order(X23,X24)
| member(esk3_2(X23,X24),X24)
| member(esk5_2(X23,X24),X24) )
& ( pre_order(X23,X24)
| member(esk3_2(X23,X24),X24)
| member(esk4_2(X23,X24),X24) )
& ( ~ pre_order(X17,X18)
| apply(X17,X20,X22)
| ~ apply(X17,X21,X22)
| ~ apply(X17,X20,X21)
| ~ member(X22,X18)
| ~ member(X21,X18)
| ~ member(X20,X18) )
& ( ~ pre_order(X17,X18)
| apply(X17,X19,X19)
| ~ member(X19,X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[pre_order])])])])])])]) ).
cnf(c_0_11,hypothesis,
( ~ subset(X1,X2)
| apply(subset_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_13,hypothesis,
( ~ member(X1,X3)
| ~ apply(subset_predicate,X3,X2)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( ~ apply(X1,esk3_2(X1,X2),esk3_2(X1,X2))
| pre_order(X1,X2)
| apply(X1,esk5_2(X1,X2),esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
apply(subset_predicate,X1,X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,hypothesis,
( ~ member(X2,esk5_2(subset_predicate,X1))
| member(X2,esk6_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_17,plain,
( ~ apply(X1,esk3_2(X1,X2),esk3_2(X1,X2))
| pre_order(X1,X2)
| apply(X1,esk4_2(X1,X2),esk5_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
( ~ member(esk2_2(X2,esk6_2(subset_predicate,X1)),esk5_2(subset_predicate,X1))
| subset(X2,esk6_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_19,hypothesis,
( ~ member(X2,esk4_2(subset_predicate,X1))
| member(X2,esk5_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_15])]) ).
cnf(c_0_20,hypothesis,
( ~ member(esk2_2(X2,esk6_2(subset_predicate,X1)),esk4_2(subset_predicate,X1))
| subset(X2,esk6_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_21,negated_conjecture,
~ ! [X4] : pre_order(subset_predicate,power_set(X4)),
inference(assume_negation,[status(cth)],[thIV18a]) ).
cnf(c_0_22,hypothesis,
( subset(esk4_2(subset_predicate,X1),esk6_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
fof(c_0_23,negated_conjecture,
~ pre_order(subset_predicate,power_set(esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_24,plain,
( ~ apply(X1,esk3_2(X1,X2),esk3_2(X1,X2))
| ~ apply(X1,esk4_2(X1,X2),esk6_2(X1,X2))
| pre_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,hypothesis,
( apply(subset_predicate,esk4_2(subset_predicate,X1),esk6_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ pre_order(subset_predicate,power_set(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,hypothesis,
pre_order(subset_predicate,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET807+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:39:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % new_bool_3 with pid 254168 completed with status 0
% 0.15/0.44 % Result found by new_bool_3
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.44 % Search class: FGUNF-FFMF21-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % SubtermCWHack with pid 254171 completed with status 0
% 0.15/0.44 % Result found by SubtermCWHack
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.44 % Search class: FGUNF-FFMF21-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % Preprocessing time : 0.001 s
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 18
% 0.15/0.44 % Removed by relevancy pruning/SinE : 13
% 0.15/0.44 % Initial clauses : 22
% 0.15/0.44 % Removed in clause preprocessing : 0
% 0.15/0.44 % Initial clauses in saturation : 22
% 0.15/0.44 % Processed clauses : 78
% 0.15/0.44 % ...of these trivial : 0
% 0.15/0.44 % ...subsumed : 15
% 0.15/0.44 % ...remaining for further processing : 63
% 0.15/0.44 % Other redundant clauses eliminated : 0
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 0
% 0.15/0.44 % Backward-rewritten : 29
% 0.15/0.44 % Generated clauses : 132
% 0.15/0.44 % ...of the previous two non-redundant : 124
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 0
% 0.15/0.44 % Paramodulations : 132
% 0.15/0.44 % Factorizations : 0
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 0
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 34
% 0.15/0.44 % ...of those cached : 28
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 34
% 0.15/0.44 % Positive orientable unit clauses : 3
% 0.15/0.44 % Positive unorientable unit clauses: 0
% 0.15/0.44 % Negative unit clauses : 0
% 0.15/0.44 % Non-unit-clauses : 31
% 0.15/0.44 % Current number of unprocessed clauses: 68
% 0.15/0.44 % ...number of literals in the above : 281
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 29
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 300
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 251
% 0.15/0.44 % Non-unit clause-clause subsumptions : 15
% 0.15/0.44 % Unit Clause-clause subsumption calls : 21
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 5
% 0.15/0.44 % BW rewrite match successes : 3
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 4227
% 0.15/0.44 % Search garbage collected termcells : 507
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.005 s
% 0.15/0.44 % System time : 0.004 s
% 0.15/0.44 % Total time : 0.009 s
% 0.15/0.44 % Maximum resident set size: 3664 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.006 s
% 0.15/0.44 % System time : 0.010 s
% 0.15/0.44 % Total time : 0.016 s
% 0.15/0.44 % Maximum resident set size: 4608 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------