%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET979+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 02:15:53 PM UTC 2026
% Result : Theorem 0.08s 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 2 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t132_zfmisc_1,conjecture,
! [X1,X2,X3] :
( cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2)))
& cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
fof(t120_zfmisc_1,axiom,
! [X1,X2,X3] :
( cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
& cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_enumset1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2)))
& cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3)) ),
inference(assume_negation,[status(cth)],[t132_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
( cartesian_product2(esk3_0,unordered_pair(esk1_0,esk2_0)) != set_union2(cartesian_product2(esk3_0,singleton(esk1_0)),cartesian_product2(esk3_0,singleton(esk2_0)))
| cartesian_product2(unordered_pair(esk1_0,esk2_0),esk3_0) != set_union2(cartesian_product2(singleton(esk1_0),esk3_0),cartesian_product2(singleton(esk2_0),esk3_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_5,plain,
! [X10,X11,X12] :
( cartesian_product2(X12,set_union2(X10,X11)) = set_union2(cartesian_product2(X12,X10),cartesian_product2(X12,X11))
& cartesian_product2(set_union2(X10,X11),X12) = set_union2(cartesian_product2(X10,X12),cartesian_product2(X11,X12)) ),
inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).
fof(c_0_6,plain,
! [X13,X14] : unordered_pair(X13,X14) = set_union2(singleton(X13),singleton(X14)),
inference(variable_rename,[status(thm)],[t41_enumset1]) ).
cnf(c_0_7,negated_conjecture,
( cartesian_product2(esk3_0,unordered_pair(esk1_0,esk2_0)) != set_union2(cartesian_product2(esk3_0,singleton(esk1_0)),cartesian_product2(esk3_0,singleton(esk2_0)))
| cartesian_product2(unordered_pair(esk1_0,esk2_0),esk3_0) != set_union2(cartesian_product2(singleton(esk1_0),esk3_0),cartesian_product2(singleton(esk2_0),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n012.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:45:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.42 % Version: 3.5.1
% 0.08/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.42 % Starting sh5l with 300s (1) cores
% 0.08/0.42 % new_bool_3 with pid 1674935 completed with status 0
% 0.08/0.42 % Result found by new_bool_3
% 0.08/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.42 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.08/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.42 % SubtermCWHack with pid 1674938 completed with status 0
% 0.08/0.42 % Result found by SubtermCWHack
% 0.08/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.42 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.08/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.42 % Preprocessing time : 0.001 s
% 0.08/0.42
% 0.08/0.42 % Proof found!
% 0.08/0.42 % SZS status Theorem
% 0.08/0.42 % SZS output start CNFRefutation
% See solution above
% 0.08/0.42 % Parsed axioms : 10
% 0.08/0.42 % Removed by relevancy pruning/SinE : 4
% 0.08/0.42 % Initial clauses : 7
% 0.08/0.42 % Removed in clause preprocessing : 0
% 0.08/0.42 % Initial clauses in saturation : 7
% 0.08/0.42 % Processed clauses : 14
% 0.08/0.42 % ...of these trivial : 0
% 0.08/0.42 % ...subsumed : 6
% 0.08/0.42 % ...remaining for further processing : 7
% 0.08/0.42 % Other redundant clauses eliminated : 0
% 0.08/0.42 % Clauses deleted for lack of memory : 0
% 0.08/0.42 % Backward-subsumed : 0
% 0.08/0.42 % Backward-rewritten : 0
% 0.08/0.42 % Generated clauses : 14
% 0.08/0.42 % ...of the previous two non-redundant : 7
% 0.08/0.42 % ...aggressively subsumed : 0
% 0.08/0.42 % Contextual simplify-reflections : 0
% 0.08/0.42 % Paramodulations : 14
% 0.08/0.42 % Factorizations : 0
% 0.08/0.42 % NegExts : 0
% 0.08/0.42 % Equation resolutions : 0
% 0.08/0.42 % Disequality decompositions : 0
% 0.08/0.42 % Total rewrite steps : 18
% 0.08/0.42 % ...of those cached : 6
% 0.08/0.42 % Propositional unsat checks : 0
% 0.08/0.42 % Propositional check models : 0
% 0.08/0.42 % Propositional check unsatisfiable : 0
% 0.08/0.42 % Propositional clauses : 0
% 0.08/0.42 % Propositional clauses after purity: 0
% 0.08/0.42 % Propositional unsat core size : 0
% 0.08/0.42 % Propositional preprocessing time : 0.000
% 0.08/0.42 % Propositional encoding time : 0.000
% 0.08/0.42 % Propositional solver time : 0.000
% 0.08/0.42 % Success case prop preproc time : 0.000
% 0.08/0.42 % Success case prop encoding time : 0.000
% 0.08/0.42 % Success case prop solver time : 0.000
% 0.08/0.42 % Current number of processed clauses : 7
% 0.08/0.42 % Positive orientable unit clauses : 5
% 0.08/0.42 % Positive unorientable unit clauses: 2
% 0.08/0.42 % Negative unit clauses : 0
% 0.08/0.42 % Non-unit-clauses : 0
% 0.08/0.42 % Current number of unprocessed clauses: 0
% 0.08/0.42 % ...number of literals in the above : 0
% 0.08/0.42 % Current number of archived formulas : 0
% 0.08/0.42 % Current number of archived clauses : 0
% 0.08/0.42 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.42 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.42 % Non-unit clause-clause subsumptions : 0
% 0.08/0.42 % Unit Clause-clause subsumption calls : 0
% 0.08/0.42 % Rewrite failures with RHS unbound : 0
% 0.08/0.42 % BW rewrite match attempts : 5
% 0.08/0.42 % BW rewrite match successes : 2
% 0.08/0.42 % Condensation attempts : 0
% 0.08/0.42 % Condensation successes : 0
% 0.08/0.42 % Termbank termtop insertions : 520
% 0.08/0.42 % Search garbage collected termcells : 55
% 0.08/0.42
% 0.08/0.42 % -------------------------------------------------
% 0.08/0.42 % User time : 0.001 s
% 0.08/0.42 % System time : 0.003 s
% 0.08/0.42 % Total time : 0.004 s
% 0.08/0.42 % Maximum resident set size: 3636 pages
% 0.08/0.42
% 0.08/0.42 % -------------------------------------------------
% 0.08/0.42 % User time : 0.002 s
% 0.08/0.42 % System time : 0.008 s
% 0.08/0.42 % Total time : 0.009 s
% 0.08/0.42 % Maximum resident set size: 4864 pages
% 0.08/0.42 % E exiting
%------------------------------------------------------------------------------