%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET159+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 02:16:43 PM UTC 2026
% Result : Theorem 29.83s 10.54s
% Output : CNFRefutation 29.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 85 ( 34 ~; 40 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 6 sgn 24 !; 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(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(thI09,conjecture,
! [X1,X2,X6] : equal_set(union(union(X1,X2),X6),union(X1,union(X2,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI09) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(c_0_4,plain,
! [X15,X16,X17,X18,X19] :
( ( subset(X18,X19)
| ~ member(esk4_2(X18,X19),X19) )
& ( subset(X18,X19)
| member(esk4_2(X18,X19),X18) )
& ( member(X17,X16)
| ~ member(X17,X15)
| ~ subset(X15,X16) ) ),
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,plain,
! [X12,X13,X14] :
( ( member(X12,union(X13,X14))
| ~ member(X12,X14) )
& ( member(X12,union(X13,X14))
| ~ member(X12,X13) )
& ( member(X12,X14)
| member(X12,X13)
| ~ member(X12,union(X13,X14)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])])]) ).
cnf(c_0_6,plain,
( ~ member(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,plain,
( ~ member(esk4_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,plain,
( ~ member(esk4_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_13,plain,
( subset(union(X1,X2),X3)
| member(esk4_2(union(X1,X2),X3),X1)
| member(esk4_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ member(esk4_2(X1,union(X2,union(X3,X4))),X3)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_15,plain,
( subset(union(X1,X2),union(X1,X3))
| member(esk4_2(union(X1,X2),union(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2,X6] : equal_set(union(union(X1,X2),X6),union(X1,union(X2,X6))),
inference(assume_negation,[status(cth)],[thI09]) ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,plain,
subset(union(X1,X2),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ member(esk4_2(X1,union(union(X2,X3),X4)),X3)
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_20,plain,
( subset(union(X1,X2),union(X3,X2))
| member(esk4_2(union(X1,X2),union(X3,X2)),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
fof(c_0_21,negated_conjecture,
~ equal_set(union(union(esk1_0,esk2_0),esk3_0),union(esk1_0,union(esk2_0,esk3_0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_22,plain,
! [X10,X11] :
( ( equal_set(X10,X11)
| ~ subset(X11,X10)
| ~ subset(X10,X11) )
& ( ~ equal_set(X10,X11)
| subset(X11,X10) )
& ( ~ equal_set(X10,X11)
| subset(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_23,plain,
( ~ member(X1,union(X2,X3))
| member(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( ~ member(esk4_2(X1,union(X2,union(X3,X4))),X4)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_25,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
~ equal_set(union(union(esk1_0,esk2_0),esk3_0),union(esk1_0,union(esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ member(esk4_2(X1,union(X2,union(X3,X4))),union(X2,X3))
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_6,c_0_23]) ).
cnf(c_0_29,plain,
( subset(union(X1,X2),union(X3,union(X4,X2)))
| member(esk4_2(union(X1,X2),union(X3,union(X4,X2))),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_30,plain,
( ~ member(X1,union(X3,X4))
| member(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_31,plain,
( ~ member(esk4_2(X1,union(union(X2,X3),X4)),X2)
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_32,negated_conjecture,
( ~ subset(union(union(esk1_0,esk2_0),esk3_0),union(esk1_0,union(esk2_0,esk3_0)))
| ~ subset(union(esk1_0,union(esk2_0,esk3_0)),union(union(esk1_0,esk2_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
subset(union(union(X1,X2),X3),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( ~ member(esk4_2(X1,union(union(X2,X3),X4)),union(X3,X4))
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_6,c_0_30]) ).
cnf(c_0_35,plain,
( subset(union(X1,X2),union(union(X1,X3),X4))
| member(esk4_2(union(X1,X2),union(union(X1,X3),X4)),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_36,negated_conjecture,
~ subset(union(esk1_0,union(esk2_0,esk3_0)),union(union(esk1_0,esk2_0),esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_37,plain,
subset(union(X1,union(X2,X3)),union(union(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET159+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n012.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 04:57:15 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 29.83/10.54 % Version: 3.5.1
% 29.83/10.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 29.83/10.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.83/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 29.83/10.54 % Starting new_bool_3 with 300s (1) cores
% 29.83/10.54 % Starting new_bool_1 with 300s (1) cores
% 29.83/10.54 % Starting sh5l with 300s (1) cores
% 29.83/10.54 % new_bool_3 with pid 1602632 completed with status 0
% 29.83/10.54 % Result found by new_bool_3
% 29.83/10.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 29.83/10.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.83/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 29.83/10.54 % Starting new_bool_3 with 300s (1) cores
% 29.83/10.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 29.83/10.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 29.83/10.54 % Search class: FGUNF-FFSF22-SFFFFFNN
% 29.83/10.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 29.83/10.54 % Starting SubtermCWHack with 31s (1) cores
% 29.83/10.54 % SubtermCWHack with pid 1602635 completed with status 0
% 29.83/10.54 % Result found by SubtermCWHack
% 29.83/10.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 29.83/10.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.83/10.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 29.83/10.54 % Starting new_bool_3 with 300s (1) cores
% 29.83/10.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 29.83/10.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 29.83/10.54 % Search class: FGUNF-FFSF22-SFFFFFNN
% 29.83/10.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 29.83/10.54 % Starting SubtermCWHack with 31s (1) cores
% 29.83/10.54 % Preprocessing time : 0.001 s
% 29.83/10.54
% 29.83/10.54 % Proof found!
% 29.83/10.54 % SZS status Theorem
% 29.83/10.54 % SZS output start CNFRefutation
% See solution above
% 29.83/10.54 % Parsed axioms : 12
% 29.83/10.54 % Removed by relevancy pruning/SinE : 8
% 29.83/10.54 % Initial clauses : 10
% 29.83/10.54 % Removed in clause preprocessing : 0
% 29.83/10.54 % Initial clauses in saturation : 10
% 29.83/10.54 % Processed clauses : 8528
% 29.83/10.54 % ...of these trivial : 88
% 29.83/10.54 % ...subsumed : 6651
% 29.83/10.54 % ...remaining for further processing : 1789
% 29.83/10.54 % Other redundant clauses eliminated : 0
% 29.83/10.54 % Clauses deleted for lack of memory : 0
% 29.83/10.54 % Backward-subsumed : 0
% 29.83/10.54 % Backward-rewritten : 2
% 29.83/10.54 % Generated clauses : 295797
% 29.83/10.54 % ...of the previous two non-redundant : 294246
% 29.83/10.54 % ...aggressively subsumed : 0
% 29.83/10.54 % Contextual simplify-reflections : 0
% 29.83/10.54 % Paramodulations : 294933
% 29.83/10.54 % Factorizations : 864
% 29.83/10.54 % NegExts : 0
% 29.83/10.54 % Equation resolutions : 0
% 29.83/10.54 % Disequality decompositions : 0
% 29.83/10.54 % Total rewrite steps : 1490
% 29.83/10.54 % ...of those cached : 854
% 29.83/10.54 % Propositional unsat checks : 0
% 29.83/10.54 % Propositional check models : 0
% 29.83/10.54 % Propositional check unsatisfiable : 0
% 29.83/10.54 % Propositional clauses : 0
% 29.83/10.54 % Propositional clauses after purity: 0
% 29.83/10.54 % Propositional unsat core size : 0
% 29.83/10.54 % Propositional preprocessing time : 0.000
% 29.83/10.54 % Propositional encoding time : 0.000
% 29.83/10.54 % Propositional solver time : 0.000
% 29.83/10.54 % Success case prop preproc time : 0.000
% 29.83/10.54 % Success case prop encoding time : 0.000
% 29.83/10.54 % Success case prop solver time : 0.000
% 29.83/10.54 % Current number of processed clauses : 1787
% 29.83/10.54 % Positive orientable unit clauses : 900
% 29.83/10.54 % Positive unorientable unit clauses: 0
% 29.83/10.54 % Negative unit clauses : 1
% 29.83/10.54 % Non-unit-clauses : 886
% 29.83/10.54 % Current number of unprocessed clauses: 285728
% 29.83/10.54 % ...number of literals in the above : 725136
% 29.83/10.54 % Current number of archived formulas : 0
% 29.83/10.54 % Current number of archived clauses : 2
% 29.83/10.54 % Clause-clause subsumption calls (NU) : 488500
% 29.83/10.54 % Rec. Clause-clause subsumption calls : 333560
% 29.83/10.54 % Non-unit clause-clause subsumptions : 6651
% 29.83/10.54 % Unit Clause-clause subsumption calls : 245434
% 29.83/10.54 % Rewrite failures with RHS unbound : 0
% 29.83/10.54 % BW rewrite match attempts : 78339
% 29.83/10.54 % BW rewrite match successes : 2
% 29.83/10.54 % Condensation attempts : 0
% 29.83/10.54 % Condensation successes : 0
% 29.83/10.54 % Termbank termtop insertions : 8978543
% 29.83/10.54 % Search garbage collected termcells : 235
% 29.83/10.54
% 29.83/10.54 % -------------------------------------------------
% 29.83/10.54 % User time : 4.736 s
% 29.83/10.54 % System time : 0.201 s
% 29.83/10.54 % Total time : 4.937 s
% 29.83/10.54 % Maximum resident set size: 3648 pages
% 29.83/10.54
% 29.83/10.54 % -------------------------------------------------
% 29.83/10.54 % User time : 4.737 s
% 29.83/10.54 % System time : 0.206 s
% 29.83/10.54 % Total time : 4.942 s
% 29.83/10.54 % Maximum resident set size: 4864 pages
% 29.83/10.54 % E exiting
%------------------------------------------------------------------------------