%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET894+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n010.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 00:55:16 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 7 unt; 0 def)
% Number of atoms : 142 ( 72 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 169 ( 65 ~; 81 |; 16 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 129 ( 11 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tarski) ).
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_zfmisc_1) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_tarski) ).
fof(l55_zfmisc_1,axiom,
! [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(t35_zfmisc_1,conjecture,
! [X1,X2] : cartesian_product2(singleton(X1),singleton(X2)) = singleton(ordered_pair(X1,X2)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t35_zfmisc_1) ).
fof(c_0_5,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])]) ).
fof(c_0_6,plain,
! [X7,X8,X9,X10,X10,X13,X14,X7,X8,X9,X16,X17] :
( ( in(esk4_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk5_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk4_4(X7,X8,X9,X10),esk5_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14)
| in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(esk6_3(X7,X8,X9),X9)
| ~ in(X16,X7)
| ~ in(X17,X8)
| esk6_3(X7,X8,X9) != ordered_pair(X16,X17)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk7_3(X7,X8,X9),X7)
| in(esk6_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk8_3(X7,X8,X9),X8)
| in(esk6_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( esk6_3(X7,X8,X9) = ordered_pair(esk7_3(X7,X8,X9),esk8_3(X7,X8,X9))
| in(esk6_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_zfmisc_1])])])])])])]) ).
cnf(c_0_7,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(esk4_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( X1 = esk4_4(X2,X3,X4,X5)
| X4 != cartesian_product2(X2,X3)
| X2 != singleton(X1)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
( in(esk5_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( X4 = ordered_pair(esk4_4(X2,X3,X1,X4),esk5_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( esk4_4(singleton(X1),X2,X3,X4) = X1
| X3 != cartesian_product2(singleton(X1),X2)
| ~ in(X4,X3) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( X1 = esk5_4(X2,X3,X4,X5)
| X4 != cartesian_product2(X2,X3)
| X3 != singleton(X1)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
fof(c_0_14,plain,
! [X4,X5] :
( ( ~ in(esk9_2(X4,X5),X4)
| ~ in(esk9_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk9_2(X4,X5),X4)
| in(esk9_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])])]) ).
cnf(c_0_15,plain,
( ordered_pair(X1,esk5_4(singleton(X1),X2,X3,X4)) = X4
| X3 != cartesian_product2(singleton(X1),X2)
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( esk5_4(X1,singleton(X2),X3,X4) = X2
| X3 != cartesian_product2(X1,singleton(X2))
| ~ in(X4,X3) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( X1 = X2
| in(esk9_2(X1,X2),X2)
| in(esk9_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( ordered_pair(X1,X2) = X3
| X4 != cartesian_product2(singleton(X1),singleton(X2))
| ~ in(X3,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( X1 = esk9_2(X2,X3)
| X2 = X3
| in(esk9_2(X2,X3),X3)
| X2 != singleton(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_20,plain,
( ordered_pair(X1,X2) = X3
| ~ in(X3,cartesian_product2(singleton(X1),singleton(X2))) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
( esk9_2(singleton(X1),X2) = X1
| singleton(X1) = X2
| in(esk9_2(singleton(X1),X2),X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,plain,
( esk9_2(singleton(X1),cartesian_product2(singleton(X2),singleton(X3))) = ordered_pair(X2,X3)
| esk9_2(singleton(X1),cartesian_product2(singleton(X2),singleton(X3))) = X1
| singleton(X1) = cartesian_product2(singleton(X2),singleton(X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| X2 != singleton(X1) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ in(esk9_2(X1,X2),X2)
| ~ in(esk9_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,plain,
( esk9_2(singleton(X1),cartesian_product2(singleton(X2),singleton(X3))) = X1
| singleton(X1) = cartesian_product2(singleton(X2),singleton(X3))
| ordered_pair(X2,X3) != X1 ),
inference(ef,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_24]) ).
fof(c_0_28,plain,
! [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_29,plain,
( singleton(X1) = cartesian_product2(singleton(X2),singleton(X3))
| ~ in(X1,cartesian_product2(singleton(X2),singleton(X3))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_20]) ).
cnf(c_0_30,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1,X2] : cartesian_product2(singleton(X1),singleton(X2)) = singleton(ordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[t35_zfmisc_1]) ).
cnf(c_0_32,plain,
( singleton(ordered_pair(X1,X2)) = cartesian_product2(singleton(X3),singleton(X4))
| ~ in(X2,singleton(X4))
| ~ in(X1,singleton(X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_33,negated_conjecture,
cartesian_product2(singleton(esk1_0),singleton(esk2_0)) != singleton(ordered_pair(esk1_0,esk2_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_34,plain,
( singleton(ordered_pair(X1,X2)) = cartesian_product2(singleton(X3),singleton(X2))
| ~ in(X1,singleton(X3)) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
cartesian_product2(singleton(esk1_0),singleton(esk2_0)) != singleton(ordered_pair(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
singleton(ordered_pair(X1,X2)) = cartesian_product2(singleton(X1),singleton(X2)),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET894+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 16:39:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.015 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 38
% 0.22/1.41 # Proof object clause steps : 27
% 0.22/1.41 # Proof object formula steps : 11
% 0.22/1.41 # Proof object conjectures : 5
% 0.22/1.41 # Proof object clause conjectures : 2
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 9
% 0.22/1.41 # Proof object initial formulas used : 5
% 0.22/1.41 # Proof object generating inferences : 16
% 0.22/1.41 # Proof object simplifying inferences : 6
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 11
% 0.22/1.41 # Removed by relevancy pruning/SinE : 5
% 0.22/1.41 # Initial clauses : 19
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 19
% 0.22/1.41 # Processed clauses : 432
% 0.22/1.41 # ...of these trivial : 3
% 0.22/1.41 # ...subsumed : 128
% 0.22/1.41 # ...remaining for further processing : 301
% 0.22/1.41 # Other redundant clauses eliminated : 10
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 1
% 0.22/1.41 # Backward-rewritten : 53
% 0.22/1.41 # Generated clauses : 4965
% 0.22/1.41 # ...of the previous two non-trivial : 4682
% 0.22/1.41 # Contextual simplify-reflections : 84
% 0.22/1.41 # Paramodulations : 4911
% 0.22/1.41 # Factorizations : 10
% 0.22/1.41 # Equation resolutions : 44
% 0.22/1.41 # Current number of processed clauses : 246
% 0.22/1.41 # Positive orientable unit clauses : 2
% 0.22/1.41 # Positive unorientable unit clauses: 0
% 0.22/1.41 # Negative unit clauses : 2
% 0.22/1.41 # Non-unit-clauses : 242
% 0.22/1.41 # Current number of unprocessed clauses: 2791
% 0.22/1.41 # ...number of literals in the above : 14827
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 54
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 19669
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 7797
% 0.22/1.41 # Non-unit clause-clause subsumptions : 165
% 0.22/1.41 # Unit Clause-clause subsumption calls : 111
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 17
% 0.22/1.41 # BW rewrite match successes : 17
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 102486
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.151 s
% 0.22/1.41 # System time : 0.008 s
% 0.22/1.41 # Total time : 0.159 s
% 0.22/1.41 # Maximum resident set size: 7792 pages
% 0.22/23.41 eprover: CPU time limit exceeded, terminating
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.43 eprover: CPU time limit exceeded, terminating
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.49 eprover: No such file or directory
% 0.22/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.49 eprover: No such file or directory
% 0.22/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.50 eprover: No such file or directory
%------------------------------------------------------------------------------