%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET867+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 : n026.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 02:15:39 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 46 ( 19 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 52 ( 21 ~; 20 |; 7 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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; 1 con; 0-3 aty)
% Number of variables : 25 ( 2 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t2_zfmisc_1,conjecture,
union(empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(c_0_3,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_4,plain,
! [X5,X6,X7] :
( ( X7 = empty_set
| in(esk1_1(X7),X7) )
& ( ~ in(X6,X5)
| X5 != empty_set ) ),
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)],[c_0_3])])])])])]) ).
fof(c_0_5,negated_conjecture,
union(empty_set) != empty_set,
inference(assume_negation,[status(cth)],[t2_zfmisc_1]) ).
cnf(c_0_6,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X9,X10,X11,X13,X14,X15,X16,X18] :
( ( X16 = union(X15)
| in(esk3_2(X15,X16),X16)
| in(esk4_2(X15,X16),X15) )
& ( X16 = union(X15)
| in(esk3_2(X15,X16),X16)
| in(esk3_2(X15,X16),esk4_2(X15,X16)) )
& ( X16 = union(X15)
| ~ in(X18,X15)
| ~ in(esk3_2(X15,X16),X18)
| ~ in(esk3_2(X15,X16),X16) )
& ( X10 != union(X9)
| in(X13,X10)
| ~ in(X14,X9)
| ~ in(X13,X14) )
& ( X10 != union(X9)
| ~ in(X11,X10)
| in(esk2_3(X9,X10,X11),X9) )
& ( X10 != union(X9)
| ~ in(X11,X10)
| in(X11,esk2_3(X9,X10,X11)) ) ),
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)],[d4_tarski])])])])])])]) ).
fof(c_0_8,negated_conjecture,
union(empty_set) != empty_set,
inference(fof_simplification,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( X2 = union(X1)
| in(esk3_2(X1,X2),X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
union(empty_set) != empty_set,
inference(fof_nnf,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(esk3_2(empty_set,X1),X1)
| X1 = union(empty_set) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
union(empty_set) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n026.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 05:45:22 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.44 % Version: 3.5.1
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % new_bool_3 with pid 1488291 completed with status 0
% 0.13/0.44 % Result found by new_bool_3
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.44 % Search class: FGHSF-FFSF31-SFFFFFNN
% 0.13/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.44 % SubtermCWHack with pid 1488295 completed with status 0
% 0.13/0.44 % Result found by SubtermCWHack
% 0.13/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.44 % Search class: FGHSF-FFSF31-SFFFFFNN
% 0.13/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.44 % Preprocessing time : 0.001 s
% 0.13/0.44
% 0.13/0.44 % Proof found!
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.44 % Parsed axioms : 7
% 0.13/0.44 % Removed by relevancy pruning/SinE : 0
% 0.13/0.44 % Initial clauses : 13
% 0.13/0.44 % Removed in clause preprocessing : 0
% 0.13/0.44 % Initial clauses in saturation : 13
% 0.13/0.44 % Processed clauses : 12
% 0.13/0.44 % ...of these trivial : 0
% 0.13/0.44 % ...subsumed : 0
% 0.13/0.44 % ...remaining for further processing : 12
% 0.13/0.44 % Other redundant clauses eliminated : 2
% 0.13/0.44 % Clauses deleted for lack of memory : 0
% 0.13/0.44 % Backward-subsumed : 0
% 0.13/0.44 % Backward-rewritten : 0
% 0.13/0.44 % Generated clauses : 8
% 0.13/0.44 % ...of the previous two non-redundant : 6
% 0.13/0.44 % ...aggressively subsumed : 0
% 0.13/0.44 % Contextual simplify-reflections : 0
% 0.13/0.44 % Paramodulations : 6
% 0.13/0.44 % Factorizations : 0
% 0.13/0.44 % NegExts : 0
% 0.13/0.44 % Equation resolutions : 2
% 0.13/0.44 % Disequality decompositions : 0
% 0.13/0.44 % Total rewrite steps : 0
% 0.13/0.44 % ...of those cached : 0
% 0.13/0.44 % Propositional unsat checks : 0
% 0.13/0.44 % Propositional check models : 0
% 0.13/0.44 % Propositional check unsatisfiable : 0
% 0.13/0.44 % Propositional clauses : 0
% 0.13/0.44 % Propositional clauses after purity: 0
% 0.13/0.44 % Propositional unsat core size : 0
% 0.13/0.44 % Propositional preprocessing time : 0.000
% 0.13/0.44 % Propositional encoding time : 0.000
% 0.13/0.44 % Propositional solver time : 0.000
% 0.13/0.44 % Success case prop preproc time : 0.000
% 0.13/0.44 % Success case prop encoding time : 0.000
% 0.13/0.44 % Success case prop solver time : 0.000
% 0.13/0.44 % Current number of processed clauses : 10
% 0.13/0.44 % Positive orientable unit clauses : 2
% 0.13/0.44 % Positive unorientable unit clauses: 0
% 0.13/0.44 % Negative unit clauses : 3
% 0.13/0.44 % Non-unit-clauses : 5
% 0.13/0.44 % Current number of unprocessed clauses: 7
% 0.13/0.44 % ...number of literals in the above : 22
% 0.13/0.44 % Current number of archived formulas : 0
% 0.13/0.44 % Current number of archived clauses : 0
% 0.13/0.44 % Clause-clause subsumption calls (NU) : 5
% 0.13/0.44 % Rec. Clause-clause subsumption calls : 5
% 0.13/0.44 % Non-unit clause-clause subsumptions : 0
% 0.13/0.44 % Unit Clause-clause subsumption calls : 0
% 0.13/0.44 % Rewrite failures with RHS unbound : 0
% 0.13/0.44 % BW rewrite match attempts : 0
% 0.13/0.44 % BW rewrite match successes : 0
% 0.13/0.44 % Condensation attempts : 0
% 0.13/0.44 % Condensation successes : 0
% 0.13/0.44 % Termbank termtop insertions : 802
% 0.13/0.44 % Search garbage collected termcells : 236
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.004 s
% 0.13/0.44 % System time : 0.003 s
% 0.13/0.44 % Total time : 0.007 s
% 0.13/0.44 % Maximum resident set size: 3632 pages
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.005 s
% 0.13/0.44 % System time : 0.008 s
% 0.13/0.44 % Total time : 0.012 s
% 0.13/0.44 % Maximum resident set size: 4608 pages
% 0.13/0.44 % E exiting
%------------------------------------------------------------------------------