%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET696+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 : n016.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 02:15:01 PM UTC 2026
% Result : Theorem 0.15s 0.55s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 32 ~; 25 |; 13 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 7 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
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(thI28,conjecture,
! [X1,X4] :
( subset(X1,X4)
=> equal_set(intersection(difference(X4,X1),X1),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI28) ).
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_6,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_7,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_8,plain,
! [X11,X12,X13] :
( ( member(X11,intersection(X12,X13))
| ~ member(X11,X13)
| ~ member(X11,X12) )
& ( ~ member(X11,intersection(X12,X13))
| member(X11,X13) )
& ( ~ member(X11,intersection(X12,X13))
| member(X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])])]) ).
fof(c_0_9,plain,
! [X17,X18,X19,X20,X21] :
( ( subset(X20,X21)
| ~ member(esk3_2(X20,X21),X21) )
& ( subset(X20,X21)
| member(esk3_2(X20,X21),X20) )
& ( member(X19,X18)
| ~ member(X19,X17)
| ~ subset(X17,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)],[subset])])])])])])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X4] :
( subset(X1,X4)
=> equal_set(intersection(difference(X4,X1),X1),empty_set) ),
inference(assume_negation,[status(cth)],[thI28]) ).
fof(c_0_11,plain,
! [X10] : ~ member(X10,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_12,plain,
! [X14,X15,X16] :
( ( member(X14,difference(X16,X15))
| member(X14,X15)
| ~ member(X14,X16) )
& ( ~ member(X14,difference(X16,X15))
| ~ member(X14,X15) )
& ( ~ member(X14,difference(X16,X15))
| member(X14,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_13,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
( ~ equal_set(intersection(difference(esk2_0,esk1_0),esk1_0),empty_set)
& subset(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_16,plain,
! [X8,X9] :
( ( equal_set(X8,X9)
| ~ subset(X9,X8)
| ~ subset(X8,X9) )
& ( ~ equal_set(X8,X9)
| subset(X9,X8) )
& ( ~ equal_set(X8,X9)
| subset(X8,X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_17,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( subset(intersection(X1,X2),X3)
| member(esk3_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
~ equal_set(intersection(difference(esk2_0,esk1_0),esk1_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_24,plain,
( ~ member(esk3_2(intersection(difference(X1,X2),X3),X4),X2)
| subset(intersection(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( subset(intersection(X1,X2),X3)
| member(esk3_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
~ subset(intersection(difference(esk2_0,esk1_0),esk1_0),empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
subset(intersection(difference(X1,X2),X2),X3),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
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 : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:37:39 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.15/0.55 % Version: 3.5.1
% 0.15/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.55 % Starting sh5l with 300s (1) cores
% 0.15/0.55 % new_bool_3 with pid 1666099 completed with status 0
% 0.15/0.55 % Result found by new_bool_3
% 0.15/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.55 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.15/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.55 % SubtermCWHack with pid 1666107 completed with status 0
% 0.15/0.55 % Result found by SubtermCWHack
% 0.15/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.55 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.15/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.55 % Preprocessing time : 0.002 s
% 0.15/0.55
% 0.15/0.55 % Proof found!
% 0.15/0.55 % SZS status Theorem
% 0.15/0.55 % SZS output start CNFRefutation
% See solution above
% 0.15/0.55 % Parsed axioms : 12
% 0.15/0.55 % Removed by relevancy pruning/SinE : 6
% 0.15/0.55 % Initial clauses : 15
% 0.15/0.55 % Removed in clause preprocessing : 0
% 0.15/0.55 % Initial clauses in saturation : 15
% 0.15/0.55 % Processed clauses : 156
% 0.15/0.55 % ...of these trivial : 1
% 0.15/0.55 % ...subsumed : 43
% 0.15/0.55 % ...remaining for further processing : 112
% 0.15/0.55 % Other redundant clauses eliminated : 0
% 0.15/0.55 % Clauses deleted for lack of memory : 0
% 0.15/0.55 % Backward-subsumed : 0
% 0.15/0.55 % Backward-rewritten : 1
% 0.15/0.55 % Generated clauses : 533
% 0.15/0.55 % ...of the previous two non-redundant : 502
% 0.15/0.55 % ...aggressively subsumed : 0
% 0.15/0.55 % Contextual simplify-reflections : 0
% 0.15/0.55 % Paramodulations : 533
% 0.15/0.55 % Factorizations : 0
% 0.15/0.55 % NegExts : 0
% 0.15/0.55 % Equation resolutions : 0
% 0.15/0.55 % Disequality decompositions : 0
% 0.15/0.55 % Total rewrite steps : 22
% 0.15/0.55 % ...of those cached : 2
% 0.15/0.55 % Propositional unsat checks : 0
% 0.15/0.55 % Propositional check models : 0
% 0.15/0.55 % Propositional check unsatisfiable : 0
% 0.15/0.55 % Propositional clauses : 0
% 0.15/0.55 % Propositional clauses after purity: 0
% 0.15/0.55 % Propositional unsat core size : 0
% 0.15/0.55 % Propositional preprocessing time : 0.000
% 0.15/0.55 % Propositional encoding time : 0.000
% 0.15/0.55 % Propositional solver time : 0.000
% 0.15/0.55 % Success case prop preproc time : 0.000
% 0.15/0.55 % Success case prop encoding time : 0.000
% 0.15/0.55 % Success case prop solver time : 0.000
% 0.15/0.55 % Current number of processed clauses : 111
% 0.15/0.55 % Positive orientable unit clauses : 45
% 0.15/0.55 % Positive unorientable unit clauses: 0
% 0.15/0.55 % Negative unit clauses : 2
% 0.15/0.55 % Non-unit-clauses : 64
% 0.15/0.55 % Current number of unprocessed clauses: 361
% 0.15/0.55 % ...number of literals in the above : 739
% 0.15/0.55 % Current number of archived formulas : 0
% 0.15/0.55 % Current number of archived clauses : 1
% 0.15/0.55 % Clause-clause subsumption calls (NU) : 396
% 0.15/0.55 % Rec. Clause-clause subsumption calls : 394
% 0.15/0.55 % Non-unit clause-clause subsumptions : 33
% 0.15/0.55 % Unit Clause-clause subsumption calls : 90
% 0.15/0.55 % Rewrite failures with RHS unbound : 0
% 0.15/0.55 % BW rewrite match attempts : 79
% 0.15/0.55 % BW rewrite match successes : 1
% 0.15/0.55 % Condensation attempts : 0
% 0.15/0.55 % Condensation successes : 0
% 0.15/0.55 % Termbank termtop insertions : 8136
% 0.15/0.55 % Search garbage collected termcells : 263
% 0.15/0.55
% 0.15/0.55 % -------------------------------------------------
% 0.15/0.55 % User time : 0.022 s
% 0.15/0.55 % System time : 0.006 s
% 0.15/0.55 % Total time : 0.028 s
% 0.15/0.55 % Maximum resident set size: 3648 pages
% 0.15/0.55
% 0.15/0.55 % -------------------------------------------------
% 0.15/0.55 % User time : 0.024 s
% 0.15/0.55 % System time : 0.012 s
% 0.15/0.55 % Total time : 0.037 s
% 0.15/0.55 % Maximum resident set size: 4864 pages
% 0.15/0.55 % E exiting
%------------------------------------------------------------------------------