TSTP Solution File: SEU165+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n007.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 09:17:22 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 81 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 32 ~; 33 |; 7 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 14 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t69_enumset1) ).
fof(t106_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t106_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l55_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).
fof(c_0_5,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_6,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
inference(assume_negation,[status(cth)],[t106_zfmisc_1]) ).
fof(c_0_8,lemma,
! [X5,X6,X7,X8,X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])])])]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( ( ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) )
& ( in(esk1_0,esk3_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) )
& ( in(esk2_0,esk4_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,lemma,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_15,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| in(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( ~ in(esk2_0,esk4_0)
| ~ in(esk1_0,esk3_0)
| ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,lemma,
( in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( in(esk2_0,esk4_0)
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_20,lemma,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0)
| ~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_23,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X3,X3)),cartesian_product2(X4,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( in(unordered_pair(unordered_pair(esk2_0,esk1_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0))
| in(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,lemma,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_26,negated_conjecture,
( in(esk1_0,esk3_0)
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk2_0,esk1_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) ),
inference(rw,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
in(esk2_0,esk4_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,lemma,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X1,X1)),cartesian_product2(X2,X4)) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( in(unordered_pair(unordered_pair(esk2_0,esk1_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0))
| in(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_31,lemma,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk2_0,esk1_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk1_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
in(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,lemma,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_35,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk2_0,esk1_0),unordered_pair(esk1_0,esk1_0)),cartesian_product2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_36,lemma,
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(X1,X4)
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 21:15:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.022 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 38
% 0.24/1.42 # Proof object clause steps : 27
% 0.24/1.42 # Proof object formula steps : 11
% 0.24/1.42 # Proof object conjectures : 17
% 0.24/1.42 # Proof object clause conjectures : 14
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 9
% 0.24/1.42 # Proof object initial formulas used : 5
% 0.24/1.42 # Proof object generating inferences : 6
% 0.24/1.42 # Proof object simplifying inferences : 17
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 95
% 0.24/1.42 # Removed by relevancy pruning/SinE : 26
% 0.24/1.42 # Initial clauses : 123
% 0.24/1.42 # Removed in clause preprocessing : 3
% 0.24/1.42 # Initial clauses in saturation : 120
% 0.24/1.42 # Processed clauses : 765
% 0.24/1.42 # ...of these trivial : 47
% 0.24/1.42 # ...subsumed : 444
% 0.24/1.42 # ...remaining for further processing : 274
% 0.24/1.42 # Other redundant clauses eliminated : 102
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 2
% 0.24/1.42 # Backward-rewritten : 36
% 0.24/1.42 # Generated clauses : 3359
% 0.24/1.42 # ...of the previous two non-trivial : 2485
% 0.24/1.42 # Contextual simplify-reflections : 79
% 0.24/1.42 # Paramodulations : 3215
% 0.24/1.42 # Factorizations : 14
% 0.24/1.42 # Equation resolutions : 130
% 0.24/1.42 # Current number of processed clauses : 231
% 0.24/1.42 # Positive orientable unit clauses : 49
% 0.24/1.42 # Positive unorientable unit clauses: 3
% 0.24/1.42 # Negative unit clauses : 20
% 0.24/1.42 # Non-unit-clauses : 159
% 0.24/1.42 # Current number of unprocessed clauses: 1615
% 0.24/1.42 # ...number of literals in the above : 4542
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 41
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 11963
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 9376
% 0.24/1.42 # Non-unit clause-clause subsumptions : 391
% 0.24/1.42 # Unit Clause-clause subsumption calls : 1664
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 62
% 0.24/1.42 # BW rewrite match successes : 24
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 31364
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.098 s
% 0.24/1.42 # System time : 0.001 s
% 0.24/1.42 # Total time : 0.099 s
% 0.24/1.42 # Maximum resident set size: 5108 pages
%------------------------------------------------------------------------------