%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET977+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 : n004.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 02:15:53 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 63 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 36 ~; 21 |; 11 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 3 con; 0-2 aty)
% Number of variables : 49 ( 4 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t130_zfmisc_1,conjecture,
! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(X1,singleton(X2)) != empty_set
& cartesian_product2(singleton(X2),X1) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t128_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
<=> ( in(X2,X4)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(t129_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( X2 = X4
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(X1,singleton(X2)) != empty_set
& cartesian_product2(singleton(X2),X1) != empty_set ) ),
inference(assume_negation,[status(cth)],[t130_zfmisc_1]) ).
fof(c_0_5,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14] :
( ( in(ordered_pair(X11,X12),cartesian_product2(singleton(X13),X14))
| ~ in(X12,X14)
| X11 != X13 )
& ( ~ in(ordered_pair(X11,X12),cartesian_product2(singleton(X13),X14))
| in(X12,X14) )
& ( ~ in(ordered_pair(X11,X12),cartesian_product2(singleton(X13),X14))
| X11 = X13 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t128_zfmisc_1])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(X1,singleton(X2)) != empty_set
& cartesian_product2(singleton(X2),X1) != empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_8,plain,
! [X7,X8,X9] :
( ( X9 = empty_set
| in(esk3_1(X9),X9) )
& ( ~ in(X8,X7)
| X7 != 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_5])])])])])]) ).
cnf(c_0_9,plain,
( ~ in(X3,X4)
| X1 != X2
| in(ordered_pair(X1,X3),cartesian_product2(singleton(X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
( ( cartesian_product2(esk1_0,singleton(esk2_0)) = empty_set
| cartesian_product2(singleton(esk2_0),esk1_0) = empty_set )
& esk1_0 != empty_set ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_11,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X15,X16,X17,X18] :
( ( in(ordered_pair(X15,X16),cartesian_product2(X17,singleton(X18)))
| X16 != X18
| ~ in(X15,X17) )
& ( ~ in(ordered_pair(X15,X16),cartesian_product2(X17,singleton(X18)))
| X16 = X18 )
& ( ~ in(ordered_pair(X15,X16),cartesian_product2(X17,singleton(X18)))
| in(X15,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t129_zfmisc_1])])])]) ).
cnf(c_0_13,plain,
( ~ in(X2,X3)
| in(ordered_pair(X1,X2),cartesian_product2(singleton(X1),X3)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( cartesian_product2(esk1_0,singleton(esk2_0)) = empty_set
| cartesian_product2(singleton(esk2_0),esk1_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X3 != X4
| ~ in(X1,X2)
| in(ordered_pair(X1,X3),cartesian_product2(X2,singleton(X4))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(X1,esk1_0)
| cartesian_product2(esk1_0,singleton(esk2_0)) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( X1 = empty_set
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( ~ in(X1,X3)
| in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X2))) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
cartesian_product2(esk1_0,singleton(esk2_0)) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ in(X1,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:45:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % new_bool_3 with pid 2371997 completed with status 0
% 0.14/0.44 % Result found by new_bool_3
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 2372004 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 11
% 0.14/0.44 % Removed by relevancy pruning/SinE : 2
% 0.14/0.44 % Initial clauses : 15
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 15
% 0.14/0.44 % Processed clauses : 38
% 0.14/0.44 % ...of these trivial : 0
% 0.14/0.44 % ...subsumed : 10
% 0.14/0.44 % ...remaining for further processing : 28
% 0.14/0.44 % Other redundant clauses eliminated : 3
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 0
% 0.14/0.44 % Backward-rewritten : 2
% 0.14/0.44 % Generated clauses : 38
% 0.14/0.44 % ...of the previous two non-redundant : 35
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 35
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 3
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 2
% 0.14/0.44 % ...of those cached : 1
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 23
% 0.14/0.44 % Positive orientable unit clauses : 3
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 5
% 0.14/0.44 % Non-unit-clauses : 15
% 0.14/0.44 % Current number of unprocessed clauses: 12
% 0.14/0.44 % ...number of literals in the above : 32
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 2
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 61
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 61
% 0.14/0.44 % Non-unit clause-clause subsumptions : 7
% 0.14/0.44 % Unit Clause-clause subsumption calls : 13
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 1
% 0.14/0.44 % BW rewrite match successes : 1
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 1206
% 0.14/0.44 % Search garbage collected termcells : 193
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.004 s
% 0.14/0.44 % System time : 0.005 s
% 0.14/0.44 % Total time : 0.009 s
% 0.14/0.44 % Maximum resident set size: 3640 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.007 s
% 0.14/0.44 % System time : 0.008 s
% 0.14/0.44 % Total time : 0.015 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------