%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET901+1 : 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 02:15:43 PM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 102 ( 68 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 121 ( 52 ~; 41 |; 23 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 12 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t42_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
fof(l46_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
inference(assume_negation,[status(cth)],[t42_zfmisc_1]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
inference(fof_simplification,[status(thm)],[l46_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X9,X10,X11] :
( ( subset(X9,unordered_pair(X10,X11))
| X9 != unordered_pair(X10,X11) )
& ( subset(X9,unordered_pair(X10,X11))
| X9 != singleton(X11) )
& ( subset(X9,unordered_pair(X10,X11))
| X9 != singleton(X10) )
& ( subset(X9,unordered_pair(X10,X11))
| X9 != empty_set )
& ( X9 = unordered_pair(X10,X11)
| X9 = singleton(X11)
| X9 = singleton(X10)
| X9 = empty_set
| ~ subset(X9,unordered_pair(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,negated_conjecture,
( ( esk1_0 = unordered_pair(esk2_0,esk3_0)
| esk1_0 = singleton(esk3_0)
| esk1_0 = singleton(esk2_0)
| esk1_0 = empty_set
| subset(esk1_0,unordered_pair(esk2_0,esk3_0)) )
& ( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != unordered_pair(esk2_0,esk3_0) )
& ( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != singleton(esk3_0) )
& ( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != singleton(esk2_0) )
& ( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != empty_set ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_9,plain,
( X1 != singleton(X2)
| subset(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ subset(X1,unordered_pair(X2,X3))
| X1 = unordered_pair(X2,X3)
| X1 = singleton(X3)
| X1 = singleton(X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( esk1_0 = unordered_pair(esk2_0,esk3_0)
| esk1_0 = singleton(esk3_0)
| esk1_0 = singleton(esk2_0)
| esk1_0 = empty_set
| subset(esk1_0,unordered_pair(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,plain,
subset(singleton(X1),unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( empty_set = esk1_0
| singleton(esk2_0) = esk1_0
| singleton(esk3_0) = esk1_0
| unordered_pair(esk2_0,esk3_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( subset(esk1_0,unordered_pair(X1,esk3_0))
| empty_set = esk1_0
| singleton(esk2_0) = esk1_0
| unordered_pair(esk2_0,esk3_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
subset(singleton(X1),unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( empty_set = esk1_0
| singleton(esk2_0) = esk1_0
| unordered_pair(esk2_0,esk3_0) = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != singleton(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( subset(esk1_0,unordered_pair(esk2_0,X1))
| empty_set = esk1_0
| unordered_pair(esk2_0,esk3_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_22,plain,
! [X12] : subset(X12,X12),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_23,negated_conjecture,
( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != unordered_pair(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( empty_set = esk1_0
| unordered_pair(esk2_0,esk3_0) = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
( ~ subset(esk1_0,unordered_pair(esk2_0,esk3_0))
| esk1_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
empty_set = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,plain,
subset(empty_set,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ subset(esk1_0,unordered_pair(esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_31,plain,
subset(esk1_0,unordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:44:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43 % Version: 3.5.1
% 0.09/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % Starting sh5l with 300s (1) cores
% 0.09/0.43 % new_bool_1 with pid 266017 completed with status 0
% 0.09/0.43 % Result found by new_bool_1
% 0.09/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.43 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.09/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.43 % SubtermCWHack with pid 266024 completed with status 0
% 0.09/0.43 % Result found by SubtermCWHack
% 0.09/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.43 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.09/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.43 % Preprocessing time : 0.001 s
% 0.09/0.43
% 0.09/0.43 % Proof found!
% 0.09/0.43 % SZS status Theorem
% 0.09/0.43 % SZS output start CNFRefutation
% See solution above
% 0.09/0.43 % Parsed axioms : 7
% 0.09/0.43 % Removed by relevancy pruning/SinE : 0
% 0.09/0.43 % Initial clauses : 15
% 0.09/0.43 % Removed in clause preprocessing : 0
% 0.09/0.43 % Initial clauses in saturation : 15
% 0.09/0.43 % Processed clauses : 31
% 0.09/0.43 % ...of these trivial : 2
% 0.09/0.43 % ...subsumed : 1
% 0.09/0.43 % ...remaining for further processing : 28
% 0.09/0.43 % Other redundant clauses eliminated : 4
% 0.09/0.43 % Clauses deleted for lack of memory : 0
% 0.09/0.43 % Backward-subsumed : 9
% 0.09/0.43 % Backward-rewritten : 6
% 0.09/0.43 % Generated clauses : 48
% 0.09/0.43 % ...of the previous two non-redundant : 35
% 0.09/0.43 % ...aggressively subsumed : 0
% 0.09/0.43 % Contextual simplify-reflections : 2
% 0.09/0.43 % Paramodulations : 44
% 0.09/0.43 % Factorizations : 0
% 0.09/0.43 % NegExts : 0
% 0.09/0.43 % Equation resolutions : 4
% 0.09/0.43 % Disequality decompositions : 0
% 0.09/0.43 % Total rewrite steps : 17
% 0.09/0.43 % ...of those cached : 10
% 0.09/0.43 % Propositional unsat checks : 0
% 0.09/0.43 % Propositional check models : 0
% 0.09/0.43 % Propositional check unsatisfiable : 0
% 0.09/0.43 % Propositional clauses : 0
% 0.09/0.43 % Propositional clauses after purity: 0
% 0.09/0.43 % Propositional unsat core size : 0
% 0.09/0.43 % Propositional preprocessing time : 0.000
% 0.09/0.43 % Propositional encoding time : 0.000
% 0.09/0.43 % Propositional solver time : 0.000
% 0.09/0.43 % Success case prop preproc time : 0.000
% 0.09/0.43 % Success case prop encoding time : 0.000
% 0.09/0.43 % Success case prop solver time : 0.000
% 0.09/0.43 % Current number of processed clauses : 9
% 0.09/0.43 % Positive orientable unit clauses : 7
% 0.09/0.43 % Positive unorientable unit clauses: 1
% 0.09/0.43 % Negative unit clauses : 1
% 0.09/0.43 % Non-unit-clauses : 0
% 0.09/0.43 % Current number of unprocessed clauses: 19
% 0.09/0.43 % ...number of literals in the above : 69
% 0.09/0.43 % Current number of archived formulas : 0
% 0.09/0.43 % Current number of archived clauses : 15
% 0.09/0.43 % Clause-clause subsumption calls (NU) : 14
% 0.09/0.43 % Rec. Clause-clause subsumption calls : 12
% 0.09/0.43 % Non-unit clause-clause subsumptions : 9
% 0.09/0.43 % Unit Clause-clause subsumption calls : 3
% 0.09/0.43 % Rewrite failures with RHS unbound : 0
% 0.09/0.43 % BW rewrite match attempts : 3
% 0.09/0.43 % BW rewrite match successes : 2
% 0.09/0.43 % Condensation attempts : 0
% 0.09/0.43 % Condensation successes : 0
% 0.09/0.43 % Termbank termtop insertions : 1231
% 0.09/0.43 % Search garbage collected termcells : 181
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.005 s
% 0.09/0.43 % System time : 0.001 s
% 0.09/0.43 % Total time : 0.006 s
% 0.09/0.43 % Maximum resident set size: 3632 pages
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.006 s
% 0.09/0.43 % System time : 0.005 s
% 0.09/0.43 % Total time : 0.012 s
% 0.09/0.43 % Maximum resident set size: 4608 pages
% 0.09/0.43 % E exiting
%------------------------------------------------------------------------------