TSTP Solution File: SET968+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.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 00:55:46 EDT 2022
% Result : Theorem 0.25s 1.42s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t121_zfmisc_1,conjecture,
! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t121_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_xboole_0) ).
fof(t4_xboole_1,axiom,
! [X1,X2,X3] : set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_xboole_1) ).
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/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t120_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
inference(assume_negation,[status(cth)],[t121_zfmisc_1]) ).
fof(c_0_5,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_6,plain,
! [X4,X5,X6] : set_union2(set_union2(X4,X5),X6) = set_union2(X4,set_union2(X5,X6)),
inference(variable_rename,[status(thm)],[t4_xboole_1]) ).
fof(c_0_7,negated_conjecture,
cartesian_product2(set_union2(esk1_0,esk2_0),set_union2(esk3_0,esk4_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk1_0,esk4_0)),cartesian_product2(esk2_0,esk3_0)),cartesian_product2(esk2_0,esk4_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
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,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
cartesian_product2(set_union2(esk1_0,esk2_0),set_union2(esk3_0,esk4_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk1_0,esk4_0)),cartesian_product2(esk2_0,esk3_0)),cartesian_product2(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,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_13,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_14,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_9 ).
cnf(c_0_15,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
c_0_10 ).
cnf(c_0_16,negated_conjecture,
$false,
inference(ar,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_13]),c_0_10]),c_0_10]),c_0_10]),c_0_10]),c_0_14,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 02:10:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.25/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.42 # Preprocessing time : 0.014 s
% 0.25/1.42
% 0.25/1.42 # Proof found!
% 0.25/1.42 # SZS status Theorem
% 0.25/1.42 # SZS output start CNFRefutation
% See solution above
% 0.25/1.42 # Proof object total steps : 17
% 0.25/1.42 # Proof object clause steps : 8
% 0.25/1.42 # Proof object formula steps : 9
% 0.25/1.42 # Proof object conjectures : 5
% 0.25/1.42 # Proof object clause conjectures : 2
% 0.25/1.42 # Proof object formula conjectures : 3
% 0.25/1.42 # Proof object initial clauses used : 5
% 0.25/1.42 # Proof object initial formulas used : 4
% 0.25/1.42 # Proof object generating inferences : 0
% 0.25/1.42 # Proof object simplifying inferences : 8
% 0.25/1.42 # Training examples: 0 positive, 0 negative
% 0.25/1.42 # Parsed axioms : 9
% 0.25/1.42 # Removed by relevancy pruning/SinE : 4
% 0.25/1.42 # Initial clauses : 6
% 0.25/1.42 # Removed in clause preprocessing : 0
% 0.25/1.42 # Initial clauses in saturation : 6
% 0.25/1.42 # Processed clauses : 11
% 0.25/1.42 # ...of these trivial : 2
% 0.25/1.42 # ...subsumed : 0
% 0.25/1.42 # ...remaining for further processing : 8
% 0.25/1.42 # Other redundant clauses eliminated : 0
% 0.25/1.42 # Clauses deleted for lack of memory : 0
% 0.25/1.42 # Backward-subsumed : 0
% 0.25/1.42 # Backward-rewritten : 1
% 0.25/1.42 # Generated clauses : 38
% 0.25/1.42 # ...of the previous two non-trivial : 19
% 0.25/1.42 # Contextual simplify-reflections : 0
% 0.25/1.42 # Paramodulations : 38
% 0.25/1.42 # Factorizations : 0
% 0.25/1.42 # Equation resolutions : 0
% 0.25/1.42 # Current number of processed clauses : 7
% 0.25/1.42 # Positive orientable unit clauses : 6
% 0.25/1.42 # Positive unorientable unit clauses: 1
% 0.25/1.42 # Negative unit clauses : 0
% 0.25/1.42 # Non-unit-clauses : 0
% 0.25/1.42 # Current number of unprocessed clauses: 14
% 0.25/1.42 # ...number of literals in the above : 14
% 0.25/1.42 # Current number of archived formulas : 0
% 0.25/1.42 # Current number of archived clauses : 1
% 0.25/1.42 # Clause-clause subsumption calls (NU) : 0
% 0.25/1.42 # Rec. Clause-clause subsumption calls : 0
% 0.25/1.42 # Non-unit clause-clause subsumptions : 0
% 0.25/1.42 # Unit Clause-clause subsumption calls : 2
% 0.25/1.42 # Rewrite failures with RHS unbound : 0
% 0.25/1.42 # BW rewrite match attempts : 19
% 0.25/1.42 # BW rewrite match successes : 11
% 0.25/1.42 # Condensation attempts : 0
% 0.25/1.42 # Condensation successes : 0
% 0.25/1.42 # Termbank termtop insertions : 666
% 0.25/1.42
% 0.25/1.42 # -------------------------------------------------
% 0.25/1.42 # User time : 0.011 s
% 0.25/1.42 # System time : 0.004 s
% 0.25/1.42 # Total time : 0.015 s
% 0.25/1.42 # Maximum resident set size: 2768 pages
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