%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 02:18:56 PM UTC 2026
% Result : Theorem 0.24s 0.58s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 119 ( 88 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 145 ( 65 ~; 50 |; 24 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 13 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t75_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_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/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( X1 != unordered_pair(X2,X3)
& X1 != singleton(X3)
& X1 != singleton(X2)
& X1 != empty_set ) ),
inference(assume_negation,[status(cth)],[t75_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] :
( set_difference(X1,unordered_pair(X2,X3)) = empty_set
<=> ~ ( 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,
! [X6,X7,X8] :
( ( subset(X6,unordered_pair(X7,X8))
| X6 != unordered_pair(X7,X8) )
& ( subset(X6,unordered_pair(X7,X8))
| X6 != singleton(X8) )
& ( subset(X6,unordered_pair(X7,X8))
| X6 != singleton(X7) )
& ( subset(X6,unordered_pair(X7,X8))
| X6 != empty_set )
& ( X6 = unordered_pair(X7,X8)
| X6 = singleton(X8)
| X6 = singleton(X7)
| X6 = empty_set
| ~ subset(X6,unordered_pair(X7,X8)) ) ),
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,plain,
! [X12,X13] :
( ( set_difference(X12,X13) = empty_set
| ~ subset(X12,X13) )
& ( subset(X12,X13)
| set_difference(X12,X13) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])])]) ).
fof(c_0_9,negated_conjecture,
( ( esk3_0 = unordered_pair(esk4_0,esk5_0)
| esk3_0 = singleton(esk5_0)
| esk3_0 = singleton(esk4_0)
| esk3_0 = empty_set
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) = empty_set )
& ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_0 != unordered_pair(esk4_0,esk5_0) )
& ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_0 != singleton(esk5_0) )
& ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_0 != singleton(esk4_0) )
& ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_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_10,plain,
( X1 != singleton(X2)
| subset(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( esk3_0 = unordered_pair(esk4_0,esk5_0)
| esk3_0 = singleton(esk5_0)
| esk3_0 = singleton(esk4_0)
| esk3_0 = empty_set
| set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,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_14,negated_conjecture,
( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_0 != singleton(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
subset(singleton(X1),unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( empty_set = esk3_0
| singleton(esk5_0) = esk3_0
| singleton(esk4_0) = esk3_0
| unordered_pair(esk4_0,esk5_0) = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_18,plain,
( X1 != singleton(X2)
| subset(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0))
| singleton(esk5_0) != esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( subset(esk3_0,unordered_pair(X1,esk5_0))
| empty_set = esk3_0
| singleton(esk4_0) = esk3_0
| unordered_pair(esk4_0,esk5_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_0 != singleton(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,plain,
subset(singleton(X1),unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( empty_set = esk3_0
| singleton(esk4_0) = esk3_0
| unordered_pair(esk4_0,esk5_0) = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_0 != unordered_pair(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0))
| singleton(esk4_0) != esk3_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_26,negated_conjecture,
( subset(esk3_0,unordered_pair(esk4_0,X1))
| empty_set = esk3_0
| unordered_pair(esk4_0,esk5_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X11] : subset(X11,X11),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_28,negated_conjecture,
( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set
| esk3_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
( ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0))
| unordered_pair(esk4_0,esk5_0) != esk3_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_30,negated_conjecture,
( empty_set = esk3_0
| unordered_pair(esk4_0,esk5_0) = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_31,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( X1 != empty_set
| subset(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
( ~ subset(esk3_0,unordered_pair(esk4_0,esk5_0))
| empty_set != esk3_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_34,negated_conjecture,
empty_set = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,plain,
subset(empty_set,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
~ subset(esk3_0,unordered_pair(esk4_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_37,plain,
subset(esk3_0,unordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_35,c_0_34]) ).
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
% 0.00/0.05 % Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.46 % Computer : n001.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Mon Sep 21 05:49:44 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.24/0.58 % Version: 3.5.1
% 0.24/0.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.58 % Starting sh5l with 300s (1) cores
% 0.24/0.58 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2316552 completed with status 0
% 0.24/0.58 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.24/0.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.58 % No SInE strategy applied
% 0.24/0.58 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.24/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.24/0.58 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/0.58 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.58 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.58 % SubtermCWHack with pid 2316556 completed with status 0
% 0.24/0.58 % Result found by SubtermCWHack
% 0.24/0.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.58 % No SInE strategy applied
% 0.24/0.58 % Search class: FGHSS-FFSS21-SFFFFFNN
% 0.24/0.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.58 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.58 % Preprocessing time : 0.001 s
% 0.24/0.58
% 0.24/0.58 % Proof found!
% 0.24/0.58 % SZS status Theorem
% 0.24/0.58 % SZS output start CNFRefutation
% See solution above
% 0.24/0.58 % Parsed axioms : 8
% 0.24/0.58 % Removed by relevancy pruning/SinE : 0
% 0.24/0.58 % Initial clauses : 17
% 0.24/0.58 % Removed in clause preprocessing : 0
% 0.24/0.58 % Initial clauses in saturation : 17
% 0.24/0.58 % Processed clauses : 37
% 0.24/0.58 % ...of these trivial : 2
% 0.24/0.58 % ...subsumed : 1
% 0.24/0.58 % ...remaining for further processing : 34
% 0.24/0.58 % Other redundant clauses eliminated : 4
% 0.24/0.58 % Clauses deleted for lack of memory : 0
% 0.24/0.58 % Backward-subsumed : 9
% 0.24/0.58 % Backward-rewritten : 12
% 0.24/0.58 % Generated clauses : 57
% 0.24/0.58 % ...of the previous two non-redundant : 48
% 0.24/0.58 % ...aggressively subsumed : 0
% 0.24/0.58 % Contextual simplify-reflections : 3
% 0.24/0.58 % Paramodulations : 53
% 0.24/0.58 % Factorizations : 0
% 0.24/0.58 % NegExts : 0
% 0.24/0.58 % Equation resolutions : 4
% 0.24/0.58 % Disequality decompositions : 0
% 0.24/0.58 % Total rewrite steps : 24
% 0.24/0.58 % ...of those cached : 17
% 0.24/0.58 % Propositional unsat checks : 0
% 0.24/0.58 % Propositional check models : 0
% 0.24/0.58 % Propositional check unsatisfiable : 0
% 0.24/0.58 % Propositional clauses : 0
% 0.24/0.58 % Propositional clauses after purity: 0
% 0.24/0.58 % Propositional unsat core size : 0
% 0.24/0.58 % Propositional preprocessing time : 0.000
% 0.24/0.58 % Propositional encoding time : 0.000
% 0.24/0.58 % Propositional solver time : 0.000
% 0.24/0.58 % Success case prop preproc time : 0.000
% 0.24/0.58 % Success case prop encoding time : 0.000
% 0.24/0.58 % Success case prop solver time : 0.000
% 0.24/0.58 % Current number of processed clauses : 9
% 0.24/0.58 % Positive orientable unit clauses : 7
% 0.24/0.58 % Positive unorientable unit clauses: 1
% 0.24/0.58 % Negative unit clauses : 1
% 0.24/0.58 % Non-unit-clauses : 0
% 0.24/0.58 % Current number of unprocessed clauses: 28
% 0.24/0.58 % ...number of literals in the above : 88
% 0.24/0.58 % Current number of archived formulas : 0
% 0.24/0.58 % Current number of archived clauses : 21
% 0.24/0.58 % Clause-clause subsumption calls (NU) : 51
% 0.24/0.58 % Rec. Clause-clause subsumption calls : 31
% 0.24/0.58 % Non-unit clause-clause subsumptions : 10
% 0.24/0.58 % Unit Clause-clause subsumption calls : 3
% 0.24/0.58 % Rewrite failures with RHS unbound : 0
% 0.24/0.58 % BW rewrite match attempts : 3
% 0.24/0.58 % BW rewrite match successes : 2
% 0.24/0.58 % Condensation attempts : 0
% 0.24/0.58 % Condensation successes : 0
% 0.24/0.58 % Termbank termtop insertions : 1413
% 0.24/0.58 % Search garbage collected termcells : 206
% 0.24/0.58
% 0.24/0.58 % -------------------------------------------------
% 0.24/0.58 % User time : 0.006 s
% 0.24/0.58 % System time : 0.005 s
% 0.24/0.58 % Total time : 0.011 s
% 0.24/0.58 % Maximum resident set size: 3632 pages
% 0.24/0.58
% 0.24/0.58 % -------------------------------------------------
% 0.24/0.58 % User time : 0.027 s
% 0.24/0.58 % System time : 0.016 s
% 0.24/0.58 % Total time : 0.043 s
% 0.24/0.58 % Maximum resident set size: 4608 pages
% 0.24/0.58 % E exiting
%------------------------------------------------------------------------------