%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET889+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n016.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 00:55:14 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 118 ( 77 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 122 ( 39 ~; 68 |; 10 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 83 ( 17 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_tarski) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l4_zfmisc_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_r1_tarski) ).
fof(t30_zfmisc_1,conjecture,
! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t30_zfmisc_1) ).
fof(c_0_5,plain,
! [X5,X6,X7,X8,X8,X5,X6,X7] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk2_3(X5,X6,X7) != X5
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk2_3(X5,X6,X7) != X6
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk2_3(X5,X6,X7),X7)
| esk2_3(X5,X6,X7) = X5
| esk2_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
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_tarski])])])])])])]) ).
fof(c_0_6,plain,
! [X3,X4,X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(X4)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])])])]) ).
fof(c_0_7,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| ~ subset(esk3_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk3_2(X4,X5),X5)
| subset(esk3_2(X4,X5),X4)
| X5 = powerset(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_zfmisc_1])])])])])])]) ).
cnf(c_0_8,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( X1 = powerset(X2)
| subset(esk3_2(X2,X1),X2)
| in(esk3_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| X3 = X2
| ~ in(X2,unordered_pair(X3,X1)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( esk3_2(singleton(X1),X2) = singleton(X1)
| esk3_2(singleton(X1),X2) = empty_set
| X2 = powerset(singleton(X1))
| in(esk3_2(singleton(X1),X2),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( esk3_2(singleton(X1),unordered_pair(X2,X3)) = singleton(X1)
| esk3_2(singleton(X1),unordered_pair(X2,X3)) = empty_set
| esk3_2(singleton(X1),unordered_pair(X2,X3)) = X2
| esk3_2(singleton(X1),unordered_pair(X2,X3)) = X3
| unordered_pair(X2,X3) = powerset(singleton(X1)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( esk3_2(singleton(X1),unordered_pair(X2,X3)) = singleton(X1)
| esk3_2(singleton(X1),unordered_pair(X2,X3)) = empty_set
| esk3_2(singleton(X1),unordered_pair(X2,X3)) = X3
| unordered_pair(X2,X3) = powerset(singleton(X1))
| X2 != empty_set ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_15,plain,
( esk3_2(singleton(X1),unordered_pair(empty_set,X2)) = singleton(X1)
| esk3_2(singleton(X1),unordered_pair(empty_set,X2)) = empty_set
| esk3_2(singleton(X1),unordered_pair(empty_set,X2)) = X2
| unordered_pair(empty_set,X2) = powerset(singleton(X1)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_16,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
( esk3_2(singleton(X1),unordered_pair(empty_set,X2)) = empty_set
| esk3_2(singleton(X1),unordered_pair(empty_set,X2)) = X2
| unordered_pair(empty_set,X2) = powerset(singleton(X1))
| singleton(X1) != X2 ),
inference(ef,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X3] : subset(X3,X3),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_19,plain,
( in(X1,X2)
| X2 != unordered_pair(X3,X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(assume_negation,[status(cth)],[t30_zfmisc_1]) ).
cnf(c_0_22,plain,
( X1 = powerset(X2)
| ~ subset(esk3_2(X2,X1),X2)
| ~ in(esk3_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,plain,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,plain,
( esk3_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = singleton(X1)
| esk3_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = empty_set
| powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| X2 != unordered_pair(X1,X3) ),
inference(er,[status(thm)],[c_0_20]) ).
fof(c_0_28,negated_conjecture,
powerset(singleton(esk1_0)) != unordered_pair(empty_set,singleton(esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_29,plain,
( X1 = powerset(singleton(X2))
| esk3_2(singleton(X2),X1) != empty_set
| ~ in(esk3_2(singleton(X2),X1),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( esk3_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = empty_set
| powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
powerset(singleton(esk1_0)) != unordered_pair(empty_set,singleton(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET889+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.06/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n016.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 Jul 10 04:34:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42 # Preprocessing time : 0.015 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 35
% 0.23/1.42 # Proof object clause steps : 24
% 0.23/1.42 # Proof object formula steps : 11
% 0.23/1.42 # Proof object conjectures : 5
% 0.23/1.42 # Proof object clause conjectures : 2
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 9
% 0.23/1.42 # Proof object initial formulas used : 5
% 0.23/1.42 # Proof object generating inferences : 12
% 0.23/1.42 # Proof object simplifying inferences : 9
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 11
% 0.23/1.42 # Removed by relevancy pruning/SinE : 0
% 0.23/1.42 # Initial clauses : 22
% 0.23/1.42 # Removed in clause preprocessing : 0
% 0.23/1.42 # Initial clauses in saturation : 22
% 0.23/1.42 # Processed clauses : 1619
% 0.23/1.42 # ...of these trivial : 47
% 0.23/1.42 # ...subsumed : 1178
% 0.23/1.42 # ...remaining for further processing : 394
% 0.23/1.42 # Other redundant clauses eliminated : 168
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 14
% 0.23/1.42 # Backward-rewritten : 164
% 0.23/1.42 # Generated clauses : 5113
% 0.23/1.42 # ...of the previous two non-trivial : 4625
% 0.23/1.42 # Contextual simplify-reflections : 548
% 0.23/1.42 # Paramodulations : 4766
% 0.23/1.42 # Factorizations : 125
% 0.23/1.42 # Equation resolutions : 222
% 0.23/1.42 # Current number of processed clauses : 214
% 0.23/1.42 # Positive orientable unit clauses : 7
% 0.23/1.42 # Positive unorientable unit clauses: 1
% 0.23/1.42 # Negative unit clauses : 4
% 0.23/1.42 # Non-unit-clauses : 202
% 0.23/1.42 # Current number of unprocessed clauses: 1451
% 0.23/1.42 # ...number of literals in the above : 8465
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 178
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 50856
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 17107
% 0.23/1.42 # Non-unit clause-clause subsumptions : 1356
% 0.23/1.42 # Unit Clause-clause subsumption calls : 33
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 9
% 0.23/1.42 # BW rewrite match successes : 6
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 110003
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.194 s
% 0.23/1.42 # System time : 0.006 s
% 0.23/1.42 # Total time : 0.200 s
% 0.23/1.42 # Maximum resident set size: 5944 pages
%------------------------------------------------------------------------------