TSTP Solution File: SET979+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:55:50 EDT 2022
% Result : Theorem 0.26s 1.43s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 3 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 3 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t132_zfmisc_1,conjecture,
! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t132_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t41_enumset1) ).
fof(t120_zfmisc_1,axiom,
! [X1,X2,X3] :
( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t120_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
inference(assume_negation,[status(cth)],[t132_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
( 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))
| cartesian_product2(esk6_0,unordered_pair(esk4_0,esk5_0)) != set_union2(cartesian_product2(esk6_0,singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk5_0))) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_5,plain,
! [X3,X4] : unordered_pair(X3,X4) = set_union2(singleton(X3),singleton(X4)),
inference(variable_rename,[status(thm)],[t41_enumset1]) ).
cnf(c_0_6,negated_conjecture,
( cartesian_product2(esk6_0,unordered_pair(esk4_0,esk5_0)) != set_union2(cartesian_product2(esk6_0,singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk5_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_7,plain,
unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X4,X5,X6] :
( cartesian_product2(set_union2(X4,X5),X6) = set_union2(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
& cartesian_product2(X6,set_union2(X4,X5)) = set_union2(cartesian_product2(X6,X4),cartesian_product2(X6,X5)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[t120_zfmisc_1])])]) ).
cnf(c_0_9,negated_conjecture,
( cartesian_product2(esk6_0,set_union2(singleton(esk4_0),singleton(esk5_0))) != set_union2(cartesian_product2(esk6_0,singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk5_0)))
| cartesian_product2(set_union2(singleton(esk1_0),singleton(esk2_0)),esk3_0) != set_union2(cartesian_product2(singleton(esk1_0),esk3_0),cartesian_product2(singleton(esk2_0),esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_10,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_8]) ).
cnf(c_0_11,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_8]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jul 9 21:30:10 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.26/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.43 # Preprocessing time : 0.014 s
% 0.26/1.43
% 0.26/1.43 # Proof found!
% 0.26/1.43 # SZS status Theorem
% 0.26/1.43 # SZS output start CNFRefutation
% See solution above
% 0.26/1.43 # Proof object total steps : 13
% 0.26/1.43 # Proof object clause steps : 6
% 0.26/1.43 # Proof object formula steps : 7
% 0.26/1.43 # Proof object conjectures : 6
% 0.26/1.43 # Proof object clause conjectures : 3
% 0.26/1.43 # Proof object formula conjectures : 3
% 0.26/1.43 # Proof object initial clauses used : 4
% 0.26/1.43 # Proof object initial formulas used : 3
% 0.26/1.43 # Proof object generating inferences : 0
% 0.26/1.43 # Proof object simplifying inferences : 6
% 0.26/1.43 # Training examples: 0 positive, 0 negative
% 0.26/1.43 # Parsed axioms : 10
% 0.26/1.43 # Removed by relevancy pruning/SinE : 4
% 0.26/1.43 # Initial clauses : 7
% 0.26/1.43 # Removed in clause preprocessing : 1
% 0.26/1.43 # Initial clauses in saturation : 6
% 0.26/1.43 # Processed clauses : 11
% 0.26/1.43 # ...of these trivial : 5
% 0.26/1.43 # ...subsumed : 0
% 0.26/1.43 # ...remaining for further processing : 5
% 0.26/1.43 # Other redundant clauses eliminated : 0
% 0.26/1.43 # Clauses deleted for lack of memory : 0
% 0.26/1.43 # Backward-subsumed : 0
% 0.26/1.43 # Backward-rewritten : 1
% 0.26/1.43 # Generated clauses : 9
% 0.26/1.43 # ...of the previous two non-trivial : 6
% 0.26/1.43 # Contextual simplify-reflections : 0
% 0.26/1.43 # Paramodulations : 9
% 0.26/1.43 # Factorizations : 0
% 0.26/1.43 # Equation resolutions : 0
% 0.26/1.43 # Current number of processed clauses : 4
% 0.26/1.43 # Positive orientable unit clauses : 3
% 0.26/1.43 # Positive unorientable unit clauses: 1
% 0.26/1.43 # Negative unit clauses : 0
% 0.26/1.43 # Non-unit-clauses : 0
% 0.26/1.43 # Current number of unprocessed clauses: 1
% 0.26/1.43 # ...number of literals in the above : 1
% 0.26/1.43 # Current number of archived formulas : 0
% 0.26/1.43 # Current number of archived clauses : 2
% 0.26/1.43 # Clause-clause subsumption calls (NU) : 0
% 0.26/1.43 # Rec. Clause-clause subsumption calls : 0
% 0.26/1.43 # Non-unit clause-clause subsumptions : 0
% 0.26/1.43 # Unit Clause-clause subsumption calls : 1
% 0.26/1.43 # Rewrite failures with RHS unbound : 0
% 0.26/1.43 # BW rewrite match attempts : 11
% 0.26/1.43 # BW rewrite match successes : 7
% 0.26/1.43 # Condensation attempts : 0
% 0.26/1.43 # Condensation successes : 0
% 0.26/1.43 # Termbank termtop insertions : 528
% 0.26/1.43
% 0.26/1.43 # -------------------------------------------------
% 0.26/1.43 # User time : 0.013 s
% 0.26/1.43 # System time : 0.002 s
% 0.26/1.43 # Total time : 0.015 s
% 0.26/1.43 # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------