TSTP Solution File: SET977+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n003.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 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 3 unt; 0 def)
% Number of atoms : 58 ( 27 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 33 ~; 22 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 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 : 57 ( 15 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t128_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
<=> ( X1 = X3
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t128_zfmisc_1) ).
fof(t129_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( in(X1,X3)
& X2 = X4 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t129_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).
fof(t130_zfmisc_1,conjecture,
! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(singleton(X2),X1) != empty_set
& cartesian_product2(X1,singleton(X2)) != empty_set ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t130_zfmisc_1) ).
fof(c_0_4,plain,
! [X5,X6,X7,X8,X5,X6,X7,X8] :
( ( X5 = X7
| ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) )
& ( X5 != X7
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(singleton(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)],[t128_zfmisc_1])])])])]) ).
fof(c_0_5,plain,
! [X5,X6,X7,X8,X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) )
& ( X6 = X8
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) )
& ( ~ in(X5,X7)
| X6 != X8
| in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(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)],[t129_zfmisc_1])])])])]) ).
fof(c_0_6,plain,
! [X3,X4,X3] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk4_1(X3),X3)
| X3 = empty_set ) ),
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)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])]) ).
cnf(c_0_7,plain,
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
| ~ in(X2,X4)
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( X1 != empty_set
=> ( cartesian_product2(singleton(X2),X1) != empty_set
& cartesian_product2(X1,singleton(X2)) != empty_set ) ),
inference(assume_negation,[status(cth)],[t130_zfmisc_1]) ).
cnf(c_0_9,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
| X2 != X4
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X1),X3))
| ~ in(X2,X3) ),
inference(er,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
( esk1_0 != empty_set
& ( cartesian_product2(singleton(esk2_0),esk1_0) = empty_set
| cartesian_product2(esk1_0,singleton(esk3_0)) = empty_set ) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X2)))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( cartesian_product2(singleton(X1),X2) != empty_set
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( cartesian_product2(esk1_0,singleton(esk3_0)) = empty_set
| cartesian_product2(singleton(esk2_0),esk1_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( cartesian_product2(X1,singleton(X2)) != empty_set
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ in(X1,esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,plain,
( X1 = empty_set
| in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 22:40:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.015 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.40 # Proof object total steps : 21
% 0.22/1.40 # Proof object clause steps : 12
% 0.22/1.40 # Proof object formula steps : 9
% 0.22/1.40 # Proof object conjectures : 7
% 0.22/1.40 # Proof object clause conjectures : 4
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 6
% 0.22/1.40 # Proof object initial formulas used : 4
% 0.22/1.40 # Proof object generating inferences : 4
% 0.22/1.40 # Proof object simplifying inferences : 4
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 11
% 0.22/1.40 # Removed by relevancy pruning/SinE : 2
% 0.22/1.40 # Initial clauses : 15
% 0.22/1.40 # Removed in clause preprocessing : 0
% 0.22/1.40 # Initial clauses in saturation : 15
% 0.22/1.40 # Processed clauses : 24
% 0.22/1.40 # ...of these trivial : 0
% 0.22/1.40 # ...subsumed : 0
% 0.22/1.40 # ...remaining for further processing : 24
% 0.22/1.40 # Other redundant clauses eliminated : 2
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 0
% 0.22/1.40 # Backward-rewritten : 0
% 0.22/1.40 # Generated clauses : 20
% 0.22/1.40 # ...of the previous two non-trivial : 16
% 0.22/1.40 # Contextual simplify-reflections : 1
% 0.22/1.40 # Paramodulations : 18
% 0.22/1.40 # Factorizations : 0
% 0.22/1.40 # Equation resolutions : 2
% 0.22/1.40 # Current number of processed clauses : 22
% 0.22/1.40 # Positive orientable unit clauses : 2
% 0.22/1.40 # Positive unorientable unit clauses: 0
% 0.22/1.40 # Negative unit clauses : 4
% 0.22/1.40 # Non-unit-clauses : 16
% 0.22/1.40 # Current number of unprocessed clauses: 7
% 0.22/1.40 # ...number of literals in the above : 15
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 0
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 47
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 45
% 0.22/1.40 # Non-unit clause-clause subsumptions : 1
% 0.22/1.40 # Unit Clause-clause subsumption calls : 14
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 0
% 0.22/1.40 # BW rewrite match successes : 0
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 980
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.013 s
% 0.22/1.40 # System time : 0.004 s
% 0.22/1.40 # Total time : 0.016 s
% 0.22/1.40 # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------