%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET921+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 : 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 02:18:54 PM UTC 2026
% Result : Theorem 0.04s 5.36s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 98 ( 35 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 118 ( 47 ~; 47 |; 15 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 64 ( 4 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t64_zfmisc_1,conjecture,
! [X1,X2,X3] :
( in(X1,set_difference(X2,singleton(X3)))
<=> ( X1 != X3
& in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_3,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( in(X1,set_difference(X2,singleton(X3)))
<=> ( X1 != X3
& in(X1,X2) ) ),
inference(assume_negation,[status(cth)],[t64_zfmisc_1]) ).
fof(c_0_5,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17] :
( ( X17 = set_difference(X15,X16)
| in(esk4_3(X15,X16,X17),X17)
| ~ in(esk4_3(X15,X16,X17),X16) )
& ( X17 = set_difference(X15,X16)
| in(esk4_3(X15,X16,X17),X17)
| in(esk4_3(X15,X16,X17),X15) )
& ( X17 = set_difference(X15,X16)
| in(esk4_3(X15,X16,X17),X16)
| ~ in(esk4_3(X15,X16,X17),X15)
| ~ in(esk4_3(X15,X16,X17),X17) )
& ( X12 != set_difference(X10,X11)
| in(X14,X12)
| in(X14,X11)
| ~ in(X14,X10) )
& ( X12 != set_difference(X10,X11)
| ~ in(X13,X12)
| ~ in(X13,X11) )
& ( X12 != set_difference(X10,X11)
| ~ in(X13,X12)
| in(X13,X10) ) ),
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)],[c_0_3])])])])])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( in(X1,set_difference(X2,singleton(X3)))
<=> ( X1 != X3
& in(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( X3 != set_difference(X2,X4)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,negated_conjecture,
( ( in(esk1_0,set_difference(esk2_0,singleton(esk3_0)))
| esk1_0 != esk3_0 )
& ( in(esk1_0,set_difference(esk2_0,singleton(esk3_0)))
| in(esk1_0,esk2_0) )
& ( esk1_0 = esk3_0
| ~ in(esk1_0,esk2_0)
| ~ in(esk1_0,set_difference(esk2_0,singleton(esk3_0))) ) ),
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])])])])]) ).
fof(c_0_9,plain,
! [X19,X20,X21,X22,X23,X24] :
( ( X24 = singleton(X23)
| esk5_2(X23,X24) = X23
| in(esk5_2(X23,X24),X24) )
& ( X24 = singleton(X23)
| esk5_2(X23,X24) != X23
| ~ in(esk5_2(X23,X24),X24) )
& ( X20 != singleton(X19)
| in(X22,X20)
| X22 != X19 )
& ( X20 != singleton(X19)
| X21 = X19
| ~ in(X21,X20) ) ),
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)],[d1_tarski])])])])])])]) ).
cnf(c_0_10,plain,
( ~ in(X1,set_difference(X2,X3))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( in(esk1_0,set_difference(esk2_0,singleton(esk3_0)))
| in(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( X3 != set_difference(X4,X2)
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( ~ in(esk1_0,esk2_0)
| ~ in(esk1_0,set_difference(esk2_0,singleton(esk3_0)))
| esk1_0 = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
in(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( X4 != set_difference(X2,X3)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
( ~ in(X1,X3)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( esk1_0 != esk3_0
| in(esk1_0,set_difference(esk2_0,singleton(esk3_0))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(esk1_0,set_difference(esk2_0,singleton(esk3_0)))
| esk3_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_21,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
~ in(esk1_0,singleton(esk3_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
esk3_0 = esk1_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])]),c_0_22]) ).
cnf(c_0_25,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/5.32 % Computer : n012.cluster.edu
% 0.04/5.32 % Model : x86_64 x86_64
% 0.04/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.32 % Memory : 8046.5625MB
% 0.04/5.32 % OS : Linux 6.8.0-71-generic
% 0.04/5.32 % CPULimit : 300
% 0.04/5.32 % WCLimit : 300
% 0.04/5.32 % DateTime : Mon Sep 21 05:43:43 UTC 2026
% 0.04/5.32 % CPUTime :
% 0.04/5.32 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/5.34 Running first-order theorem proving
% 0.04/5.34 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
% 0.04/5.36 % Version: 3.5.1
% 0.04/5.36 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.04/5.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/5.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.04/5.36 % Starting new_bool_3 with 300s (1) cores
% 0.04/5.36 % Starting new_bool_1 with 300s (1) cores
% 0.04/5.36 % Starting sh5l with 300s (1) cores
% 0.04/5.36 % new_bool_3 with pid 1670662 completed with status 0
% 0.04/5.36 % Result found by new_bool_3
% 0.04/5.36 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.04/5.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/5.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.04/5.36 % Starting new_bool_3 with 300s (1) cores
% 0.04/5.36 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.04/5.36 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.04/5.36 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.04/5.36 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.04/5.36 % Starting SubtermCWHack with 31s (1) cores
% 0.04/5.36 % SubtermCWHack with pid 1670665 completed with status 0
% 0.04/5.36 % Result found by SubtermCWHack
% 0.04/5.36 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.04/5.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/5.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.04/5.36 % Starting new_bool_3 with 300s (1) cores
% 0.04/5.36 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.04/5.36 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.04/5.36 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.04/5.36 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.04/5.36 % Starting SubtermCWHack with 31s (1) cores
% 0.04/5.36 % Preprocessing time : 0.001 s
% 0.04/5.36
% 0.04/5.36 % Proof found!
% 0.04/5.36 % SZS status Theorem
% 0.04/5.36 % SZS output start CNFRefutation
% See solution above
% 0.04/5.36 % Parsed axioms : 6
% 0.04/5.36 % Removed by relevancy pruning/SinE : 2
% 0.04/5.36 % Initial clauses : 14
% 0.04/5.36 % Removed in clause preprocessing : 0
% 0.04/5.36 % Initial clauses in saturation : 14
% 0.04/5.36 % Processed clauses : 24
% 0.04/5.36 % ...of these trivial : 1
% 0.04/5.36 % ...subsumed : 0
% 0.04/5.36 % ...remaining for further processing : 23
% 0.04/5.36 % Other redundant clauses eliminated : 6
% 0.04/5.36 % Clauses deleted for lack of memory : 0
% 0.04/5.36 % Backward-subsumed : 0
% 0.04/5.36 % Backward-rewritten : 5
% 0.04/5.36 % Generated clauses : 25
% 0.04/5.36 % ...of the previous two non-redundant : 22
% 0.04/5.36 % ...aggressively subsumed : 0
% 0.04/5.36 % Contextual simplify-reflections : 1
% 0.04/5.36 % Paramodulations : 20
% 0.04/5.36 % Factorizations : 0
% 0.04/5.36 % NegExts : 0
% 0.04/5.36 % Equation resolutions : 6
% 0.04/5.36 % Disequality decompositions : 0
% 0.04/5.36 % Total rewrite steps : 12
% 0.04/5.36 % ...of those cached : 9
% 0.04/5.36 % Propositional unsat checks : 0
% 0.04/5.36 % Propositional check models : 0
% 0.04/5.36 % Propositional check unsatisfiable : 0
% 0.04/5.36 % Propositional clauses : 0
% 0.04/5.36 % Propositional clauses after purity: 0
% 0.04/5.36 % Propositional unsat core size : 0
% 0.04/5.36 % Propositional preprocessing time : 0.000
% 0.04/5.36 % Propositional encoding time : 0.000
% 0.04/5.36 % Propositional solver time : 0.000
% 0.04/5.36 % Success case prop preproc time : 0.000
% 0.04/5.36 % Success case prop encoding time : 0.000
% 0.04/5.36 % Success case prop solver time : 0.000
% 0.04/5.36 % Current number of processed clauses : 13
% 0.04/5.36 % Positive orientable unit clauses : 3
% 0.04/5.36 % Positive unorientable unit clauses: 0
% 0.04/5.36 % Negative unit clauses : 3
% 0.04/5.36 % Non-unit-clauses : 7
% 0.04/5.36 % Current number of unprocessed clauses: 10
% 0.04/5.36 % ...number of literals in the above : 31
% 0.04/5.36 % Current number of archived formulas : 0
% 0.04/5.36 % Current number of archived clauses : 5
% 0.04/5.36 % Clause-clause subsumption calls (NU) : 47
% 0.04/5.36 % Rec. Clause-clause subsumption calls : 40
% 0.04/5.36 % Non-unit clause-clause subsumptions : 1
% 0.04/5.36 % Unit Clause-clause subsumption calls : 9
% 0.04/5.36 % Rewrite failures with RHS unbound : 0
% 0.04/5.36 % BW rewrite match attempts : 2
% 0.04/5.36 % BW rewrite match successes : 2
% 0.04/5.36 % Condensation attempts : 0
% 0.04/5.36 % Condensation successes : 0
% 0.04/5.36 % Termbank termtop insertions : 1270
% 0.04/5.36 % Search garbage collected termcells : 364
% 0.04/5.36
% 0.04/5.36 % -------------------------------------------------
% 0.04/5.36 % User time : 0.004 s
% 0.04/5.36 % System time : 0.000 s
% 0.04/5.36 % Total time : 0.004 s
% 0.04/5.36 % Maximum resident set size: 3636 pages
% 0.04/5.36
% 0.04/5.36 % -------------------------------------------------
% 0.04/5.36 % User time : 0.004 s
% 0.04/5.36 % System time : 0.003 s
% 0.04/5.36 % Total time : 0.008 s
% 0.04/5.36 % Maximum resident set size: 4864 pages
% 0.04/5.36 % E exiting
%------------------------------------------------------------------------------