TSTP Solution File: SET961+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET961+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 00:55:44 EDT 2022
% Result : Theorem 0.21s 1.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 6 unt; 0 def)
% Number of atoms : 80 ( 28 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 32 ~; 37 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 14 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t114_zfmisc_1,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t114_zfmisc_1) ).
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(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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
inference(assume_negation,[status(cth)],[t114_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,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])])])])]) ).
fof(c_0_6,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk2_0,esk1_0)
& esk1_0 != empty_set
& esk2_0 != empty_set
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( in(X1,esk2_0)
| ~ in(ordered_pair(X2,X1),cartesian_product2(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,plain,
! [X4,X5] :
( ( ~ in(esk4_2(X4,X5),X4)
| ~ in(esk4_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk4_2(X4,X5),X4)
| in(esk4_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_13,negated_conjecture,
( in(X1,esk1_0)
| ~ in(ordered_pair(X1,X2),cartesian_product2(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
fof(c_0_14,plain,
! [X3,X4,X3] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk3_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_15,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk1_0)
| ~ in(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( X1 = X2
| in(esk4_2(X1,X2),X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X2,esk1_0)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_18,plain,
( X1 = empty_set
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( X1 = esk1_0
| in(esk4_2(X1,esk1_0),esk2_0)
| in(esk4_2(X1,esk1_0),X1)
| ~ in(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,plain,
( X1 = X2
| ~ in(esk4_2(X1,X2),X2)
| ~ in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( X1 = esk1_0
| in(esk4_2(X1,esk1_0),esk2_0)
| in(esk4_2(X1,esk1_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_21]) ).
cnf(c_0_25,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( X1 = esk1_0
| ~ in(esk4_2(X1,esk1_0),esk2_0)
| ~ in(esk4_2(X1,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
in(esk4_2(esk2_0,esk1_0),esk2_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET961+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.12/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n024.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 22:56:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.21/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.41 # Preprocessing time : 0.015 s
% 0.21/1.41
% 0.21/1.41 # Proof found!
% 0.21/1.41 # SZS status Theorem
% 0.21/1.41 # SZS output start CNFRefutation
% See solution above
% 0.21/1.41 # Proof object total steps : 29
% 0.21/1.41 # Proof object clause steps : 20
% 0.21/1.41 # Proof object formula steps : 9
% 0.21/1.41 # Proof object conjectures : 17
% 0.21/1.41 # Proof object clause conjectures : 14
% 0.21/1.41 # Proof object formula conjectures : 3
% 0.21/1.41 # Proof object initial clauses used : 10
% 0.21/1.41 # Proof object initial formulas used : 4
% 0.21/1.41 # Proof object generating inferences : 10
% 0.21/1.41 # Proof object simplifying inferences : 6
% 0.21/1.41 # Training examples: 0 positive, 0 negative
% 0.21/1.41 # Parsed axioms : 11
% 0.21/1.41 # Removed by relevancy pruning/SinE : 2
% 0.21/1.41 # Initial clauses : 16
% 0.21/1.41 # Removed in clause preprocessing : 0
% 0.21/1.41 # Initial clauses in saturation : 16
% 0.21/1.41 # Processed clauses : 87
% 0.21/1.41 # ...of these trivial : 2
% 0.21/1.41 # ...subsumed : 26
% 0.21/1.41 # ...remaining for further processing : 59
% 0.21/1.41 # Other redundant clauses eliminated : 0
% 0.21/1.41 # Clauses deleted for lack of memory : 0
% 0.21/1.41 # Backward-subsumed : 8
% 0.21/1.41 # Backward-rewritten : 1
% 0.21/1.41 # Generated clauses : 148
% 0.21/1.41 # ...of the previous two non-trivial : 137
% 0.21/1.41 # Contextual simplify-reflections : 6
% 0.21/1.41 # Paramodulations : 142
% 0.21/1.41 # Factorizations : 4
% 0.21/1.41 # Equation resolutions : 2
% 0.21/1.41 # Current number of processed clauses : 50
% 0.21/1.41 # Positive orientable unit clauses : 5
% 0.21/1.41 # Positive unorientable unit clauses: 0
% 0.21/1.41 # Negative unit clauses : 8
% 0.21/1.41 # Non-unit-clauses : 37
% 0.21/1.41 # Current number of unprocessed clauses: 21
% 0.21/1.41 # ...number of literals in the above : 79
% 0.21/1.41 # Current number of archived formulas : 0
% 0.21/1.41 # Current number of archived clauses : 9
% 0.21/1.41 # Clause-clause subsumption calls (NU) : 644
% 0.21/1.41 # Rec. Clause-clause subsumption calls : 426
% 0.21/1.41 # Non-unit clause-clause subsumptions : 29
% 0.21/1.41 # Unit Clause-clause subsumption calls : 44
% 0.21/1.41 # Rewrite failures with RHS unbound : 0
% 0.21/1.41 # BW rewrite match attempts : 1
% 0.21/1.41 # BW rewrite match successes : 1
% 0.21/1.41 # Condensation attempts : 0
% 0.21/1.41 # Condensation successes : 0
% 0.21/1.41 # Termbank termtop insertions : 2644
% 0.21/1.41
% 0.21/1.41 # -------------------------------------------------
% 0.21/1.41 # User time : 0.020 s
% 0.21/1.41 # System time : 0.001 s
% 0.21/1.41 # Total time : 0.021 s
% 0.21/1.41 # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------